Chapter 7 - Applications of Trigonometry and Vectors - Section 7.5 - Applications of Vectors - 7.5 Exercises - Page 343: 55

$90^{\circ}$

$\textbf u =\langle 1,2 \rangle$ $\textbf v =\langle -6,3 \rangle$ $\cos\theta=\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $ $\cos\theta=\frac{ \langle 1,2 \rangle . \langle -6,3 \rangle }{ | \sqrt {1^2+2^2}| | | \sqrt { (-6)^2+3^2} | } $ $\cos\theta=\frac{ 1\times (-6)+2\times 3 }{ | \sqrt 5| | | {\sqrt { 45} | } }$ $\cos\theta=\frac{ 0 }{ 15 }=0 $ $\cos\theta=0$ $\theta =\cos^{-1}0=90^{\circ}$