Chapter 8 - Application of Trigonometry - 8.4 Algebraically Defined Vectors and the Dot Product - 8.4 Exercises - Page 789: 12

$${\text{16;}}\,{315^ \circ }$$

$$\eqalign{ & \left\langle {8\sqrt 2 , - 8\sqrt 2 } \right\rangle \cr & {\text{The magnitude of the vector is }} \cr & \left| {\left\langle {8\sqrt 2 , - 8\sqrt 2 } \right\rangle } \right| = \sqrt {{{\left( {8\sqrt 2 } \right)}^2} + {{\left( { - 8\sqrt 2 } \right)}^2}} \cr & \left| {\left\langle {8\sqrt 2 , - 8\sqrt 2 } \right\rangle } \right| = \sqrt {128 + 128} \cr & \left| {\left\langle {8\sqrt 2 , - 8\sqrt 2 } \right\rangle } \right| = \sqrt {256} \cr & \left| {\left\langle {8\sqrt 2 , - 8\sqrt 2 } \right\rangle } \right| = 16 \cr & {\text{The direction of the vector is }} \cr & \theta = {\tan ^{ - 1}}\left( {\frac{{ - 8\sqrt 2 }}{{8\sqrt 2 }}} \right) + {360^ \circ } \cr & \theta = {315^ \circ } \cr} $$