Find he cosine of the angle between the vectors `4 hat i-3 hat j+3 hat k\ a n d\ 2 hat i- hat j- hat kdot`

Explanation

Assume,`vec{a}=4 hat{i}-3 hat{j}+3 hat{k}`


and `vec{b}=2 hat{i}-hat{j}-hat{k}`


Assume theta be the angle between `vec{a} and vec{b}`


`|vec{a}|=sqrt{(4)^{2}+(-3)^{2}+(3)^{2}}=sqrt{34}`


`|vec{b}|=sqrt{(2)^{2}+(-1)^{2}+(-1)^{2}}=sqrt{6}`


Hence` vec{a} cdot vec{b}=8+3-3=8`


`Cos theta=frac{vec{a} cdot vec{b}}{|vec{a}||vec{b}|}=frac{8}{sqrt{34} sqrt{6}}=frac{8}{2 sqrt{51}}=frac{4}{sqrt{51}}`