## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 11 - Section 11.4 - The Cross Product - Exercises - Page 623: 31

#### Answer

$(a)\quad$ Makes sense. $(b)\quad$ Does not make sense. $(c)\quad$ Makes sense. $(d)\quad$ Does not make sense.

#### Work Step by Step

$(a)\quad$ ${\bf u}\times{\bf v}$ is a vector, ${\bf w}$ is a vector. The dot product of two vectors is defined. Makes sense. $(b)\quad$ ${\bf u}$ is a vector, but ${\bf v}\cdot{\bf w}$ is not. The cross product is not defined for a vector and scalar. Does not make sense. $(c)\quad$ ${\bf u}$ is a vector, ${\bf v}\times{\bf w}$ is a vector. The dot product of two vectors is defined. Makes sense. $(d)\quad$ ${\bf v}\cdot{\bf w}$ is a scalar. The scalar product is defined between two vectors. ${\bf u}$ is a vector, but ${\bf v}\cdot{\bf w}$ is not. Does not make sense.

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