# Calculus - Orthogonal Trajectories

17,164 results

### Calculus - Orthogonal Trajectories

Find the orthogonal trajectories of the family of curves: y = k*(e^-x) --------------- so k = y/(e^-x) differentiating we get: 1 = -k(e^-x)*(dx/dy) 1/(dx/dy) = -k(e^-x) dy/dx = -k(e^-x)...substituting for k: dy/dx = -(y/(e^-x))*(e^-x) dy/dx = -y Integral(1/=y)dy = Integral dx...

### calc 2

Find the orthogonal trajectories for the family of curves y=(kx)^6.

### math

Find the orthogonal trajectories of family of the circle x2+y2=a2 where a is a parameter

### Math

Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. If A is an n*n symmetric orthogonal matrix ...

### calculus

two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and to show the tangent lines

### Calculus

What is the orthogonal trajectory of y^2 - x^2 = C ??

### Math - Vectors

Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?

### calculus

if the tangent of two intersecting circles, at their points of intersection are perpendicular, the circles are said to be orthogonal. Show that the circles x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal. find the equation of the tangent to the ellipse x^2/a^2 + y^2/b^...

### Linear Algebra, orthogonal

The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 matrices

### Calculus

Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].

### Calculus

Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].

### Calculus

Find the orthoganal trajectories of the family. Use a graphing utility to graph several members of each family. y = Ce^x What am I supposed to do here? Can someone point me in the right direction?

### linear algebra

Hello, how can I proof the next theorem? I have a linear transformation T(X) that can be express as T(X)=AX and A is an orthogonal matrix, then ||T (X)||=||X|| , I was doing this: ||T (X)||=sqrt(<AX,AX>) But I don't know what to do with the orthogonal matrix.. Please help

### Math

I'm doing a bunch of practice finals and I don't know how to approach this problem. Find a vector a such that a is orthogonal to < 1, 5, 2 > and has length equal to 6. If I want to find a vector that is orthogonal to <1,5,2>, I must take the cross product?

### Linear Algebra

Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square orthogonal matrix then B^−1 = B^T. (d) If for ...

### calculus

Find an equation of the plane orthogonal to the line (x,y,z)=(-4,-9,9)+t(-8,-1,5) which passes through the point (-9,9,-4). Give your answer in the form ax+by+cz=d.

### Calculus

Determine whether the planes are parallel or orthogonal. Equations given: 5x - 3y + z = 4 x + 4y + 7z = 1 How exactly do I solve this? It wasn't covered completely in class.

### Calculus

Find an equation of the plane orthogonal to the line: (x,y,z) = (5,-6,-1) + t(3,10,-3) which passes through the point (-6,-1,5). so i got so far: x=5+3t y=-6+10t z=-1-3t Should be in form ax+by+cz+d=d Not sure where to go from there...

### calculus (vectors)

Determine a vector that is orthogonal to the vector e = [3, -1, 4]

### Calculus-PLZ help!

Given u=3i-2j+k,v=2i-4j-3k, w=-i+2j+2k, 1 Find a unit vector normal to the plane containing v and w. 2 Find the volume of the parallelepiped formed by u, v, and w. 3 Are any of these vectors parallel? Orthogonal? Why or why not?

### Precalculus

Latex: The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. Regular: The vector <k, 2>, is orthogonal to the vector <3, 5>. Find k. I can't seem to figure it out, I thought k would be 10/3

### calculus

I have 3 points: P(-3, 1, 2), Q(-1, 2, 3), R(2, 1, 0) and I need to find a nonzero vector orthogonal to the plane through these three points. I seem to recall this having something to do with the cross product, so I mad vectors PQ <2,1,1> & PR <5,0,-2> calculated ...

### math

Show that x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal.

### st joseph

show that the circle x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal

### linear algebra

Solve for x if the vectors (2, x, 7-x) and (x, 3, -2) are orthogonal

### Diagonalize

construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible. Just write down a diagonal matrix with one zero on the diagonal and then apply an orthogonal transformation. E.g. if you start with the matrix: A = [1 ,0 0,1] And take the orthogonal transformation...

### Vectors

Determine a unit vector that is orthogonal to both u=[3,-4, 1] and v=[2,3,-4].

### Math

Determine whether u and v are orthogonal,parallel, or neither. u=-2i+j v=3i+6j

### Calc

Determine whether u and v are orthogonal, parallel or neither u= <-4, 7>, v= <-14, 12>

### calc

If possible, find a, b, and c so that v = [a b c] is orthogonal to both w = [1 6 1] and x = [1 −9 1]

### Math

Knowing u = (4,0,-3), v = (x,3,2) and that the orthogonal projection of v on u is a vector of norm 6, determine x. Thank you

### math

Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)

### Math

Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)

### Algebra

Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)

### mathematics

find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.

### Math

Find the orthogonal trajectory of the family of circle x^2 (y-c)^2 c^2 where c is parameter.

### Algebra

Determine if the following two planes 2x+3y-z=4 and 3x-4y-6z=1 are parallel, orthogonal or coincidental

### Linear Algebra

Knowing u = (4,0,-3), v = (x,3,2) and that the orthogonal projection of v on u is a vector of norm 6, determine x. Thank you

### Math

Find an equation of a plane through the point (1, 5, 1) which is orthogonal to the line x=3+5t y=5-1t z=-1+4t in which the coefficient of x is 5.

### Math

How do we know the ith of an invertible matrix B is orthogonal to the jth column of B^-1 , if i is not equal/unequal to j?

### physics

A particle is moving in a circular trajectory because of a magnetic field. Show that regardless of the veolocity of the particle, it will take the same amount of time to complete one revolution. I'm not sure how to prove this. Should i use the formula for circle trajectories.....

### TRIGONOMETRY

Use the dot product to determine which of the following vector pairs are orthogonal. a. v1 = (-5,5) and v2 = (1,1) b. v1 = (154,169.4) and v2 = (88,64)

### Linear Algebra

A test Question: Find the parametric equations of the line through the origin that is orthogonal to the plane 2x+4y-z=0

### Geometry/Algebra/Calculus

Why isn't the surface area of a sphere with radius r the following: 2*pi * (pi*r) That comes from the following flow of logic: Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semi-circle with radius r, pi*r (2*pi*...

### Math

The functional determinant of x, e^x, and e^-x is equal to___ The orthogonal trajectory of y^2 - x^2 = C is__ The slope of the normal line to y^2 = x/2 at P(1/8,1/4) is ____ help please...

### Dr. D ram D.A.V. Public school

A parabola y²=4x cuts the circle with centre at (6,5) orthogonal then the possible points of intersection between the curves are?

### Neurology

Which of the following pairs of terms identify spaces that are roughly PERPENDICULAR (orthogonal) in the human brain (give or take 30 degrees or so)?

### mathematical physics

Determine the scale factors for an orthogonal coordinate system (s,t,v) whose coordinates are related to the Cartesian by the following equations: x = 2st, y = s^2-t^2, z = v.

### rotational mechanics

a thin rod of length 2R and mass M is standing vertically on a perfectly smooth floor. the state of equilibrium in which the rod at rest is unstable and the rod falls. FInd the trajectories that the various points of rod describe and velocity with which the upper end of rod ...

### math

Diagonalize the given matrix and find an orthogonal matrix P such that P−1AP is diagonal -2 3 3 3 -2 3 3 3 -2

### math

A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x, ..., sin nx } Use ...

### math urgent

let V=R^3 and S={u1,u2,u3}=[1;2;0],[1;0;0],[1;0;1] These are three vectors 1 by 3 use gschmidt to obtain an orthogonal basis and then find the coordinates of x=[1;2;3] relative to this basis.

### vectors

how do you determine if two vectors are a) Collinear b) orthogonal?

### math

Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing another solution which is ...

### Art History

In linear perspective, all parallel lines converge at a(n): A. orthogonal. B. vanishing point. C. horizon line. D. picture plane. OK, my textbook says it both A and C so I am totally confused.

### math

) Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these.

### physics

Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. One is a robust 250 g beast initially moving south at 20.0 cm/s, while the other is a svelte 150 g creature initially moving north at 60.0 ...

### mathematical physics

Determine the scale factors for an orthogonal coordinate system ( s, t, v ) whose coordinates are related to the cartesion by following equations: x = 2st:, y = s^2-t^2:, z = v Also write down an expression for the square of the arc element.

### mathematical physics

Determine the scale factors for an orthogonal coordinate system (s, t, v) whose coordinates are related to the Cartesian by the following equations: x = 2st, y = s^2-t^2, z = v Also write down an expression for the square of the arc element.

### linear algebra urgent

For the orthogonal matrix A = 1/sqrt(2) -1/sqrt(2) -1/(sqrt(2)) -1/sqrt(2) verify that (Ax,Ay)=(x,y) for any vectors x and y in R2. Can someone please explain this

### math

can an inner product space v have a t invariant subspace U but also have an orthogonal complement that is NOT t-invariant???

### math

Find the least squares approximation of x over the interval [0,1] by a polynomial of the form a + b*e^x --------------------------------------------------------- The polynomial produces an output space with two linearly independent basis vectors: u1 = 1, u2 = e^x I believe ...

### Linear Algebra

Find the basis for the following vector space. Please state the dimension of the vector space. S consists of all x in R3 such that x is orthogonal to n=(2,3,2)

### math

Find the orthogonal canonical reduction of the quadratic from -x^2+y^2+z^2-6xy+2yz. Also, find its principal axes,rank and signature of the quadratic form.

### math

Find the orthogonal canonical reduction of the quadratic from -x^2+y^2+z^2-6xy+2yz. Also, find its principal axes,rank and signature of the quadratic form.

### physics

An electron starting from rest acquires 4.20 keV of kinetic energy in moving from point A to point B. How much kinetic energy would a proton acquire, starting from rest at B and moving to point A? Determine the ratio of their speeds at the end of their respective trajectories.

### math

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?

### Physics

Two projectiles are launched from ground level at the same angle above the horizontal, and both return to ground level. Projectile A has a launch speed that is twice that of projectile B. (Sketch trajectories of projectiles). Assuming that air resistance is absent, what should...

### math

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?

### math

There is one step in a proof that I don't understand. Could someone please explain? u = any vector in vector space S W = finite dimensional subspace of S with orthonormal basis of vectors {v1, v2, ..., vn} The theorem to prove is: u can be expressed exactly one way as u = w1...

### Math

Show that A = [3 2 4 2 0 2 4 2 3] is distinguishable even though one eigenvector has algebraic multiplicity 2. Do this by brute force computation. Why would you expect this to be true, even without calculation? Then, for the A, write A= Q lambda Q^(T) where Q's columns are ...

### Math

1. P5 is an innerproduct space with an inner product. We applied the Gram Schmidt process tot he basis {1,x,x^2,x^3,x^4} and obtained the following as the result {f1,f2,f3,f4,x^4+2}. a. What is the orthogonal complement of P3 in P5 with erspect to this inner product? b. What ...

### linear algebra-urgent

1)let w=[3;4] and u=[1;2] a) find the projection p of u onto w. I found this to be p=[1.32;1.76] b) find a scalar k for which the vector kp has a norm that is equal to one. k=? d)find a vector that is orthogonal to span{w} s=? how do I do this

### math

Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove what I'm looking to prove...

### Linear Algebra

Ok this is the last one I promise! It's from a sample exam and I'm practicing for my finals :) Verify if the following 4 points are consecutive vertices of a parallelogram: A(1,-1,1); B(3,0,2);C(2,3,4);D(0,2,3) (b) Find an orthogonal vector to the plane containing the ...

### Geometry

What is the relative position of two lines if their orthogonal projection onto the projection planes are a) parallel lines b) coinciding lines c) intersecting lines

### Math

cotA = tan(90degrees- A) True or False The vectors <4, 5> and <-10, 8> are orthogonal True or False 2<3, 5> = 16 True or False <2. 3>*<4, 3> = <2, 6> + <4, 5> = Find c if a = 3, b = 5, and A = 30degrees=

### Math

cotA = tan(90degrees- A) True or False The vectors <4, 5> and <-10, 8> are orthogonal True or False 2<3, 5> = 16 True or False <2. 3>*<4, 3> = <2, 6> + <4, 5> = Find c if a = 3, b = 5, and A = 30degrees=

### ART HELP!

Please help me with this: What step did the artist clearly use when drawing a two-point perspective image? A. A vanishing point *** B. Only orthogonal lines C. Imagery in the backgrounds larger than in the foreground. D. Imagery in the foreground lighter than in the background.

### ART! URGENT

What shold an artist do first in order to draw a two-point perspective image? A. Use orthogonal lines. B. Use value changes C. Draw all vertical lines D. Draw a horisan line C?

### math

The runway of an airfield faces west. An airplane, flying in the direction of north-east at a height of 2km and at a speed of 400km/h, on a path which passes over a point 3km west of the runway end, is spotted sqrt(29)km horizontally(south-western quadrant) from the runway end...

### Art

1. Which step did the artist clearly use when drawing this image? two vanishing points only orthogonal lines imagery in the background larger than in the foreground imagery in the foreground lighter than in the background 2. Because of the use of value change in this image, ...

### linear algebra

Find the inverse of each of the following orthogonal matrices. A= [1 0 0 0 cos(theta) sin(theta) 0 -sin(theta) cos(theta)]

### physics

Two bar magnets (1) and(2) orthogonal to each other create at point M (intersection of their supports) the respective magnetic field vectors B1 and B2 of intensity: B1=o.oo3T and B2=0.004T a)Determine the names of the poles of the magnets. b)Construct the resultant field ...

### Pre-Calculus/Calculus

I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...

### Trigonometry

Which of the following pairs of vectors are orthogonal? (i) v = 18i − 3j and w = −i − 6j (ii) v = 15i − 2j and w = −4i + 30j (iii) v = 3i − j and w = i + 3j A. (i) and (ii) B. (i) and (iii) C. (ii) only D. (i) only 17.

### Finite Math

Fifty percent of students enrolled in calculus class have previously taken pre-calculus. Thirty percent of these students received an A for the calculus class, whereas twenty percent of the other students received an A for calculus. Find the probability that a student selected...

### Calc 3

Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. * I answered part a and got the correct answer with the vector <0,26,-13> I found...

### Calculus

What is the use of Calculus? How is it use in jobs? What jobs use Calculus? Calculus is used in engineering, economics, any physical science, and in business (e.g., actuary studies and statistics).

### Precalculus

The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. I thought the answer should be 10/4/

### linear algebra

3. Suppose A is symmetric positive definite and Q is an orthogonal matrix (square with orthonormal columns). True or false (with a reason or counterexample)? a) (Q^(T))AQ is a diagonal matrix b) (Q^(T))AQ is a symmetric positive definite matrix c) (Q^(T))AQ has the same ...

### linear math

Let u=(2,0,k,-1) v=(-4,0,-3,2) and w= (0,1,0,0). Each answer must be justified(there is no answer where k=nothing) a) find all values of k, (if any) for which u is orthogonal to v b) Find all values of k (if any) for which the set {u,v,w} is linearly independent. Find all ...

### math

Can I please get my answers double checked? True or False 1. The tangent function is used to find the angel between two vectors. True 2. If two vectors are orthogonal, then their dot product is -1. False 3. The length of the projected vector is always shorter than the length ...

### Calculus

Hellp I have a calculus test on Monday 2. Calculate the slope of the tangent to the given function at the given point or value of x a. f(x)=3/x+1,P(2,1) b.h(x)=2/squareroot x + 5, P(4,2/3) ****Full solutions to please because I do not know what I'm doing and so confused with ...

### Biology

Theme A: Surface anatomy of the brain Of the following pairs of directional terms, which pair contains terms that define PERPENDICULAR (orthogonal) directions when applied to the identified region of the central nervous system? in the brainstem, ventral & anterior in the ...

### Maths trigonometry

using basic trigonometry derive the following equations, which are used to convert cartesian to polar coordinates and vice versa. why is the cos(phi)in the x term? x = R cos (phi) sin (lamda) y = R sin (phi) they are used in orthogonal projection of a spherical surface to a ...

### Algebra

In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked geometry and algebra but not calculus. Of ...

### art history

1. Art enabled new understandings in this field 2. Credited with being the founder of Renaissance painting in the Netherlands 3. his most famous painting depicts sin and redemptionhe 4. brought Germany into the mainstream of Renaissance art 5. objects appear to get smaller ...

### Calculus

What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? (I know that the cycloid is the solution but I need a simple calculus proof as to why this is the case)