## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 13 - Vector Geometry - 13.2 Vectors in Three Dimensions - Exercises - Page 659: 13

#### Answer

(a) Parallel and point in the same direction. (b) Not parallel. (c) Parallel and point in the opposite direction. (d) Not parallel.

#### Work Step by Step

(a) Since $v=\langle 4,8,12\rangle = 2\langle 2,4,5\rangle$, then the vectors are parallel and have the same direction. (b) Since there is no real number $m$ such that $v=\langle 4,8,12\rangle = m\langle-1,-2,3\rangle$, then the vectors are not parallel. (c) Since $v=\langle 4,8,12\rangle = -1.75\langle-7,-14,-21\rangle$, then the vectors are parallel. However, they point in opposite directions (negative sign). (d) Since there is no real number $m$ such that $v=\langle 4,8,12\rangle = m\langle6,10,14\rangle$, then the vectors are not parallel.

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