### Home > PC > Chapter 10 > Lesson 10.1.4 > Problem10-54

10-54.

Find the angle between the vectors (find the angle in degrees).

Refer to the Math Notes box titled Dot Product.

1. $\langle - 4,5 \rangle$ and $\langle 2,7 \rangle$

$\operatorname { cos } \theta = \frac { a \cdot b } { \| a \| \| b \| }$

$a · b = \left(−4\right)\left(2\right) + \left(5\right)\left(7\right) = 27$

$\left. \begin{array} { l } { \| a \| = \sqrt { ( } ( - 4 ) ^ { 2 } + ( 5 ) ^ { 2 } ) = \sqrt { 4 } 1 } \\ { \| b \| = \sqrt { ( } ( 2 ) ^ { 2 } + ( 7 ) ^ { 2 } ) = \sqrt { 5 } 3 } \end{array} \right.$

$\theta = \operatorname { cos } ^ { - 1 } ( \frac { 27 } { \sqrt { ( 41 \cdot 53 ) } } )$

$54.6º$

1. $2\textbf{i} −3\textbf{j}$ and $−4\textbf{i} −2\textbf{j}$

Follow the steps outlined in part (a).

$97.1º$