## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 68

#### Answer

The values of the components of the vector are $-\text{258}\text{.1}\mathbf{i}\text{+368}\text{.6}\mathbf{j}$.

#### Work Step by Step

Speed of plane in the direction of north-west = 450 miles per hour. The angle of inclination of the plane in the direction of north-west $=35{}^\circ .$ The vector`s direction angle from the positive axis to V is $\theta =90{}^\circ +35{}^\circ =135{}^\circ$. The vector component along the x- axis or horizontal is i and the vector component along the y- axis or the vertical direction is j. As the plane is travelling at 450 miles per hour. So, $\left| \left| \mathbf{v} \right| \right|=450$ Therefore, the equation becomes as: \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{450cos125}{}^\circ \mathbf{i}+\text{450sin125}{}^\circ \mathbf{j} \\ & =\text{450}\left( -\text{0}\text{.57} \right)\mathbf{i}+\text{450}\left( \text{0}\text{.82} \right)\mathbf{j} \\ & =-\text{258}\text{.1}\mathbf{i}+\text{368}\text{.6}\mathbf{j} \end{align}

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