Question

Find the unit vector in the direction of vector B=4i+2j-5k​

Answer 1

Answer:

$\frac{4}{\sqrt{45} } i\,+\frac{2}{\sqrt{45} } j-\frac{5}{\sqrt{45} } k$

Explanation:

for the unit vector, we need to divide the given vector by its norm, because it should be in the SAME direction as the original vector, but of magnitude "1".

We notice that the norm of the given vector is:

$\sqrt{4^2+2^2+(-5)^2} =\sqrt{45}$

Then, the unit vector becomes:

$\frac{4}{\sqrt{45} } i\,+\frac{2}{\sqrt{45} } j-\frac{5}{\sqrt{45} } k$