Question

Find the angle (in radians) between the vectors. (Round your answer to two decimal places.)

u = (7, 3)
v=(3,0)
=

Answer 1

`~~~~~~~~~~~~\textit{angle between two vectors } \\\\ \cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}} \implies \measuredangle \theta = \cos^(-1)\left(\cfrac{u \cdot v}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u= < 7,3 > \\ v= < 3,0 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u\cdot v\implies (7)(3)~~ + ~~(3)(0)\implies 21+0\implies 21 \\\\[-0.35em] ~\dotfill`

`||u||=√( 7^2 + 3^2)\implies u=√( 49 + 9 ) \implies u=√( 58 ) \\\\\\ ||v||=√( 3^2 + 0^2)\implies ||v||=√( 9 + 0 ) \implies ||v||=√( 9 )\implies ||v||=3 \\\\[-0.35em] ~\dotfill\\\\ \theta =\cos^(-1)\left( \cfrac{21}{3√(58)} \right)\implies \theta =\cos^(-1)\left( \cfrac{7}{√(58)} \right)\implies \theta \approx 0.40~rad`

Make sure your calculator is in Radians mode.