Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.6 Vectors in Space - 8.6 Assess Your Understanding - Page 645: 28



Work Step by Step

If a vector $v$ initiates at point $A(x_1,y_1,z_1)$ and terminates at $B(x_2,y_2,z_2)$, then we can write the vector as $v =\lt x_2-x_1, y_2-y_1, z_2-z_1 \gt =(x_2-x_1)i+(y_2-y_1)j+(z_2-z_1)k.$ Here, we have: $A=(0,0,0)$ and $B=(-3,-5,4)$ Therefore, $v=(-3-0)i+(-5-0)j+(4-0)k\\ =-3i-5j+4k$
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