Ask questions and get helpful responses.
Ask a New Question
  1. Questions

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.

Here's the step by step from the book that I'm having a hard time wrapping around, perhaps someone can help me solve and suggest a rule I can review for this type of problem:

The target variables are the components of C. We are given A and B. We also know A⋅C and B⋅C, and this gives us two equations in the two unknowns Cx and Cy.

A and C are perpendicular, so A⋅C = 0. AxCx + AyCy = 0, which gives 5.0Cx − 6.5Cy = 0.
B⋅C = 15.0, so −3.5Cx + 7.0Cy = 15.0

We have two equations in two unknowns Cx and Cy. Solving gives Cx = 8.0 and Cy = 6.1.

(It's the "Solving" that has me scratching my head...)

We can check that our result does give us a vector C that satisfies the two equations A⋅C = 0 and B⋅C =15.0.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Vectors

  1. 5.0Cx − 6.5Cy = 0
    −3.5Cx + 7.0Cy = 15.0

    using determinates D= 35-22.75 = 12.25

    then x= +15*6.5 divided by 12.25
    cx= 7.96
    cy= 75/12.25=6.12

    A.C= (5*7.96-6.5*6.12)= zero
    B.C= (-3.5*7.96+7*6.12)= 15

    You don't have to use determinants, but it is pretty fast on a 2x2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    👤
    bobpursley

  2. Fantastic. I realized I've been doing this with the -2.5 instead of -3.5 as the x component of vector B, and of course it didn't make any sense. Thank you for the response!

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Vectors

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.

  2. Physics

    The sum & difference of two non-zero vectors Ä & B are equal in magnitude.what can you conclude about these vectors?why?

  3. Physics

    1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the

  4. 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. physics

    the position vectors of the head and tail of radius vectors are 2i+j+k and 2i-3j+k. the linear momomentum is 2i+3j+k. the angular momentum is

  2. Math

    Find all vectors v in 2 dimensions having ||v ||=5 where the i -component of v is 3i vectors:

  3. physic

    Three vectors are shown in the figure below, but they are not drawn to scale. The sum of the three vectors is R = F1 + F2 + F3. If Ry = 0 and F2 = 0.2F3,find Rx in terms of F1. the angle for F1 is 30 degree

  4. Calculus

    Given vectors u= (1,-1,3) and v= (-4,5,3) find an ordered triple that represents vectors 3u-2v. a.(16,1,-7) b.(11,-13,3) c.(10,-12,1) d.(7,-7,16) I don't want you to straight up give me the answer. I need someone to teach me how

  1. 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

  2. Calulas and VECTORS

    THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a * b

  3. Digital art and design

    “Lesson 1: Final Exam 0103000 M/J Digital Art and Design 1- T2 Unit 5: Final Exam. I have been stuck on this 50 question test for a while now im willing to give away a gift card if someone helps me and puts in the answers by

  4. Calculus

    Suppose vectors a and b are vectors such that a x b =(3,1,4). What is the cross product of twice of a with twice of b?

Still need help? You can ask a new question.