Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 792: 13



Work Step by Step

Find the scalar, $\left( 4\mathbf{u} \right)\cdot \mathbf{v}$ as, $\begin{align} & \left( 4\mathbf{u} \right)\cdot \mathbf{v=}\left[ 4\times \left( 2\mathbf{i-j} \right) \right]\cdot \left( 3\mathbf{i+j} \right) \\ & =\left( 8\mathbf{i-}4\mathbf{j} \right)\cdot \left( 3\mathbf{i+j} \right) \\ & =8\cdot 3+\left( -4 \right)\cdot 1 \\ & =24-4 \end{align}$ Solve ahead to get the result as, $\begin{align} & \left( 4\mathbf{u} \right)\cdot \mathbf{v}=24-4 \\ & =20 \end{align}$ Hence, the scalar of $\left( 4\mathbf{u} \right)\cdot \mathbf{v}$ is $20$.
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