Find the unit vector in the direction of `3 hat i+4 hat j-12 hat kdot`

Explanation

`\vec{a} =3 \hat{i}+4 \hat{j}-12 \hat{k}`

`|\vec{a}| =\sqrt{3^{2}+4^{2}+(-12)^{2}} \quad =\sqrt{9+16+144}=\sqrt{16 9}`

`|\vec{a}| =13`

`\hat{a} =\frac{\vec{a}}{|\vec{a}|}=\frac{3 \hat{i}+4 \hat{j}-12 \hat{k}}{13} \Rightarrow \hat{a}=\frac{3}{13} \hat{a}+\frac{4}{13} \hat{j}-\frac{12}{13}\hat{k}`