Calculus

posted by .

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 -

The normals of the two planes are
(5, -3, 1) and (1 , 4, 7)

Since one is not a multiple of the other, the two planes cannot be parallel

if they are orthogonal (perpendicular) then their dot product must be zero

so (5,-3,1)∙(1,4,7) = 5 -12 + 7 = 0
YEs, they are orthogonal

Similar Questions

1. Calculus

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. …
2. Plz Check My Geometry

Out of 30 questions these few I struggled with. I put what I feel was right but to be sure I would like some one to check my answers and if there wrong redirect me on how to get the correct answer.( after the = is the answer i think …
3. Plz Check My Geometry

Out of 30 questions these few I struggled with. I put what I feel was right but to be sure I would like some one to check my answers and if there wrong redirect me on how to get the correct answer.( after the = is the answer i think …
4. Math(Calculus)

Ok I have a bunch of questions, please bare with me and i'd appreciate it VERY much if you could help me with these! 1. Assume that you are given the equations of three planes. Without solving the system, describe a "test" with rationale, …
5. Math - intersection of planes

You are given the following two planes: x+4y-3z-12=0 x+6y-2z-22=0 a) Determine if the planes are parallel b) Fine the line of intersection of the two planes. c) Use the two original equations to determine two other equations that have …
6. Algebra

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

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

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

Consider the surface given by the equation: 2x2 - 3z2 - 4x -4y - 12z + 2 = 0 (a) Write in standard form ) (b) Determine and classify the traces with planes parallel to the xy-, xz- and yz- planes. (c) Hence classify the surface.
10. 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.

More Similar Questions