Mathematics

Mathematics

Problem

Let

\mathbf{r}=\mathbf{u}-\mathbf{v}

where

\mathbf{u}

and

\mathbf{v}

are two non–zero vectors with magnitudes

|\mathbf{u}|=a

and

|\mathbf{v}|=b

. The angle between

\mathbf{u}

and

\mathbf{v}

is

\theta

(with

0<\theta<\pi

). a. (i) Prove that

|\mathbf{r}|^{2}=a^{2}+b^{2}-2ab\cos\theta

. b. (ii) Using the result from part (i), compute

|\mathbf{r}|

when

a=12

,

b=9

and

\theta=150^{\circ}

.

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