Chapter 8 - Application of Trigonometry - 8.4 Algebraically Defined Vectors and the Dot Product - 8.4 Exercises - Page 789: 10

$${\text{25;}}\,\,{106.2^ \circ }$$

$$\eqalign{ & \left\langle { - 7,24} \right\rangle \cr & {\text{The magnitude of the vector is }} \cr & \left| {\left\langle { - 7,24} \right\rangle } \right| = \sqrt {{{\left( { - 7} \right)}^2} + {{\left( {24} \right)}^2}} \cr & \left| {\left\langle { - 7,24} \right\rangle } \right| = \sqrt {49 + 576} \cr & \left| {\left\langle { - 7,24} \right\rangle } \right| = 25 \cr & {\text{The direction of the vector is }} \cr & \theta = {\tan ^{ - 1}}\left( {\frac{{24}}{{ - 7}}} \right) + {180^ \circ } \cr & \theta \approx {106.2^ \circ } \cr} $$