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 793: 40


The scalar is $-40$.

Work Step by Step

The scalar $4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)$ can be obtained as, $\begin{align} & 4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)\mathbf{=}4\left( -\mathbf{i}+\mathbf{j} \right)\cdot \left[ 5\left( 3\mathbf{i}-2\mathbf{j} \right)-3\left( -5\mathbf{j} \right) \right] \\ & =\left( -4\mathbf{i}+4\mathbf{j} \right)\cdot \left( 15\mathbf{i}-10\mathbf{j}+15\mathbf{j} \right) \\ & =\left( -4\mathbf{i}+4\mathbf{j} \right)\cdot \left( 15\mathbf{i}+5\mathbf{j} \right) \\ & =\left( -4 \right)\cdot 15+4\cdot 5 \end{align}$ Solve ahead to get the result as, $\begin{align} & 4\mathbf{u}\cdot \left( 5\mathbf{v-}3\mathbf{w} \right)=\left( -4 \right)\cdot 15+4\cdot 5 \\ & =-60+20 \\ & =-40 \end{align}$ Hence, the scalar of $4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)$ is $-40$.
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