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: 39


The scalar is $25$.

Work Step by Step

The scalar $5\mathbf{u}\cdot \left( 3\mathbf{v-}4\mathbf{w} \right)$ can be obtained as, $\begin{align} & 5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)\mathbf{=}5\left( -\mathbf{i}+\mathbf{j} \right)\cdot \left[ 3\left( 3\mathbf{i}-2\mathbf{j} \right)-4\left( -5\mathbf{j} \right) \right] \\ & =\left( -5\mathbf{i}+5\mathbf{j} \right)\cdot \left( 9\mathbf{i}-6\mathbf{j}+20\mathbf{j} \right) \\ & =\left( -5\mathbf{i}+5\mathbf{j} \right)\cdot \left( 9\mathbf{i}+14\mathbf{j} \right) \\ & =\left( -5 \right)\cdot 9+5\cdot 14 \end{align}$ Solve ahead to get the result as, $\begin{align} & 5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)=\left( -5 \right)\cdot 9+5\cdot 14 \\ & =-45+70 \\ & =25 \end{align}$ Hence, the scalar of $5\mathbf{u}\cdot \left( 3\mathbf{v}-4\mathbf{w} \right)$ is $25$.
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