Vectors

posted by .

A=i –2j B=-3i+j How do I find the component of A that is perpendicular to B in vector form?

  • Vectors -

    A = i - 2 j so |A| = sqrt 5
    B = -3 i + j so |B| = sqrt 10

    The magnitude of the cross product A x B is |A| |B| sin T
    where T is the angle between the vectors.
    i j k
    1 -2 0
    -3 1 0 --> -5 k
    so the magnitude of the cross product is 5
    so
    sqrt 5 * sqrt 10 * sin T = 5
    5 sqrt 2 * sin T = 5
    sin T = 1/sqrt 2
    The component of A perpendicular to B, call it R, therefore has magnitude sqrt 5 /sqrt 2
    We know that it is perpendicular to B so
    B dot R has magnitude = 0
    so
    Rx Bx + RyBy = 0
    Rx(-3)+ Ry(1) = 0
    so Ry = 3 Rx
    so call it
    R = c Rx + 3c Ry where c is a constant
    magnitude = c sqrt (10)
    which has to be sqrt 5/sqrt 2
    so c sqrt 10 = sqrt 5/sqrt 2
    c = sqrt 5 /(sqrt 2*sqrt 2 * sqrt 5)
    c = 1/2 but it could be negative
    so our vector is
    R = (1/2) i + (3/2) j
    or
    R = -(1/2) i - (3/2) j
    looking at a sketch of the vectors, use the second one but both are valid.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    The two vectors a and b have equal magnitudes(on an x-y plane vector a is 30 degrees from the x axis then vector b is 75 degrees from the head of vector a it is heading towards north west) of 10m A)find the x component of their vector …
  2. science (physics) Need to solve this today please

    (a) Express the vectors A, B, and C in the figure below in terms of unit vectors. (b) Use unit vector notation to find the vectors R = A + B + C and S = C – A – B. (c) What are the magnitude and directions of vectors R and S?
  3. Math: Vectors

    Find any vector w that is perpendicular to both vector "u = 3j + 4k" and vector "v = 2i". Note: i, j and k are unit vectors How would you solve this problem?
  4. physics [vectors]

    The concept i get, but somehow i just can't execute this problem, please help me! You are given vectors A = 5.5 6.2 and B = - 3.7 7.4 . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product …
  5. maths

    Given that vector c and vector d are non zero vectors such that vector c =x1i + y1j + z1k and vector d =(y1z2-y2z1)+(x1y2 -x2y1)show that the two vectors are perpendicular.
  6. Physics

    You are given vectors A = 5.0i - 6.5j & B = -3.5i + 7.0j. A third vector C lies on the xy-plane. Vector C is perpendicular to vector A, & the scalar product of C with B is 15.0. From this information, find the components of vector …
  7. Math: Trig

    Help with vectors, please. Thanks 1) Express point in rectangular form. Give EXACT answer, if possible?
  8. Physics

    You are given vectors A = 5.0i - 6.5j and B = -2.5i + 7.0j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 15.0. Find the x and y components to vector C. Answer key …
  9. Physics

    Vectors A and B are added to produce C, that is A+B=C. If B=-5x+5y and C=2x-3y. Find the unit vector of A, that is find A (in component form).
  10. PHYSICS

    The figure shows two displacement vectors and . Vector points at an angle of 20.0° above the x axis and has an unknown magnitude. Vector has an x component Bx = 31.0 m and has an unknown y component By. These two vectors are equal. …

More Similar Questions