Answer
$$15;126.9^\circ $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle { - 9,12} \right\rangle \cr
& \cr
& {\text{Calculate the magnitude, recall that }}\left| {\left\langle {a,b} \right\rangle } \right| = \sqrt {{a^2} + {b^2}} \cr
& \left| {\bf{u}} \right| = \left| {\left\langle { - 9,12} \right\rangle } \right| = \sqrt {{{\left( { - 9} \right)}^2} + {{\left( {12} \right)}^2}} \cr
& \left| {\bf{u}} \right| = \sqrt {81 + 144} = \sqrt {225} \cr
& \left| {\bf{u}} \right| = 15 \cr
& \cr
& {\text{The direction of the angle is given by }}\theta = {\tan ^{ - 1}}\left( {\frac{b}{a}} \right) \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{12}}{{ - 9}}} \right) + 180^\circ \cr
& \theta \approx 126.9^\circ \cr} $$
