Math

if vectors a+2b and 5a-4b are perpendicular to each other and a and b are unit vectors. Find the angle between a and b.

  1. 👍 10
  2. 👎 0
  3. 👁 3,988
  1. Let θ be the angle between a and b. We know that cosθ = (a∙b) / (|a||b|). Since a and b are unit vectors, |a|=|b|=1. Therefore we need to find a∙b.

    a+2b and 5a-4b are perpendicular, so

    (a+2b)∙(5a-4b)=0

    Multiply this out to obtain

    5a∙a + 6a∙b - 8b∙b = 0

    which results in

    6a∙b = 8b∙b - 5a∙a

    Since a and b are unit vectors,

    6a∙b = 8-5 = 3

    Therefore, cos θ = 3/6. θ=π/3

    1. 👍 29
    2. 👎 10
  2. 👏😀

    1. 👍 11
    2. 👎 5
  3. Good!

    1. 👍 9
    2. 👎 2
  4. Good

    1. 👍 0
    2. 👎 1
  5. If two vectors are perpendicular their dot product will equal zero.
    (a+2b)•(5a-4b)=0
    5a•a+10a•b-4a•b-8b•b=0
    6a•b=8b•b-5a•a
    6a•b=8-5=3
    cosθ=3/6.
    θ=π/3

    1. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    Write an expression for a unit vector at 45∘ clockwise from the x-axis. Express your answer in terms of the unit vectors i^ and j^.

  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. PreCalculus

    Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors. I am just beginning the study of vectors and have this problem. Could someone help? Thanks.

  4. Physics

    A pair of 328.1 N vectors are perpendicular. What is the magnitude of their resultant? Answer in units of N.

  1. math help

    Find the unit vector perpendicular to each of the vectors 2i+j+k and i-j+2k?

  2. Vectors

    Given vectors A = -4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

  3. Physics

    What is the resultant of two displacement vectors having the same direction? a. The resultant is the sum of the two displacements having the same direction as the original vectors. b. The resultant is the difference of the two

  4. calculus

    Find parametric equations and symmetric equations for the line through P0 and perpendicular to both given vectors. (P0 corresponds to t = 0.) P0 = (4, 3, 0) i + j and j + k Not exactly sure what to do, how do I find what is

  1. physics

    Two vectors have magnitudes 3.0 and 4.0. How are the directions of the two vectors related given the following conditions? 1) The sum has magnitude 7.0. (a)They both point in the same direction. (b)They each point in opposite

  2. Math

    Given two non-collinear vectors a and b, show that a, axb, and (axb)xa are mutually perpendicular. Also Express the unit vectors i, j, and k as ordered triplets and show that i x j = k what are ordered triplets? Using components

  3. Physics

    Two horizontal vectors, 21 units North and 20 units East, are combined with a 10-unit vector vertically upwards. Find the angle between the resultant of the three vectors and the vertical one.

  4. IB Math SL

    Find a unit vector which is perpendicular to both of the vectors 4i + 2j - 3k and 2i - 3j + k.

You can view more similar questions or ask a new question.