Physics - Vectors Question with Solution | TestHub

Given $\vec{U}=0.9\hat{i}-0.2\hat{j}+m\hat{k}$ is a unit vector.

The magnitude of a unit vector is $1$.

$|\vec{U}|=\sqrt{(0.9{)}^2+(-0.2{)}^2+m^2}=1$

Squaring both sides:

$0.81+0.04+m^2=1$

$0.85+m^2=1$

$m^2=1-0.85$

$m^2=0.15$

$m=\sqrt{0.15}$

Answer: $\sqrt{0.15}$