7.4 Find the unit vector that points from point O toward point A.319A1| 37⁰Answers: nA/O=( iF = 6.5 KN133°TTi+ i+ik) Express F as a vector in terms of the unit vectors i, j, and k. Determine the projection, both as a scalar and as a vector, of F onto line OA,which lies in the x-y plane.+31°A37°F = 6.5 KN133°

Write the position vectors of points O and A.Write the position vector of the line connecting point…

Answered: Find the unit vector that points from…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

7.4

Find the unit vector that points from point O toward point A.
319
A
1
| 37⁰
Answers: nA/O=( i
F = 6.5 KN
1
33°
T
T
i+ i
+
i
k)

Express F as a vector in terms of the unit vectors i, j, and k. Determine the projection, both as a scalar and as a vector, of F onto line OA,
which lies in the x-y plane.
+
31°
A
37°
F = 6.5 KN
1
33°

Expert Solution

Step 1: Position vector

Write the position vectors of points O and A.

$table row cell bold r subscript O equals left parenthesis 0 bold i plus 0 bold j plus 0 bold k right parenthesis end cell row cell bold r subscript A equals left parenthesis cos 31 degree right parenthesis bold i plus left parenthesis sin 31 degree right parenthesis bold j plus left parenthesis 0 right parenthesis bold k end cell end table$

Write the position vector of the line connecting point O with point A.

$table row cell bold r subscript A divided by O end subscript equals bold r subscript A minus bold r subscript O end cell row cell bold r subscript A divided by O end subscript equals left square bracket left parenthesis cos 31 degree right parenthesis bold i plus left parenthesis sin 31 degree right parenthesis bold j plus left parenthesis 0 right parenthesis bold k right square bracket minus left parenthesis 0 bold i plus 0 bold j plus 0 bold k right parenthesis end cell row cell bold r subscript A divided by O end subscript equals left parenthesis cos 31 degree right parenthesis bold i plus left parenthesis sin 31 degree right parenthesis bold j end cell end table$

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