## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 69

#### Answer

The length of the shadow is $\left| \left| \text{1}\text{.4} \right| \right|\text{=1}\text{.4 inches}$.

#### Work Step by Step

The magnitude and direction of the vector are given. Analyze the vector and resolve it into its horizontal and vertical components. The vector component along the x-axis or the horizontal direction is i and the vector component along the y-axis or the vertical direction is j. Therefore, the equation becomes \begin{align} & \mathbf{v}=\left| \left| \mathbf{v} \right| \right|\text{cos}\theta \mathbf{i}+\left| \left| \mathbf{v} \right| \right|\text{sin}\theta \mathbf{j} \\ & =\text{1}\text{.5cos}25{}^\circ \mathbf{i}+\text{1}\text{.5sin}25{}^\circ \mathbf{j} \\ & =1.41\mathbf{i}+0.6\mathbf{j} \end{align} The shadow forms on the x-axis; therefore, only the horizontal component is taken and the vertical component is ignored.

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