Question

a paricle is at q(-12,-5).find the unit vector along oq?

Answer 1

A particle is at point $Q(-12, -5)$. Find the unit vector along $OQ$.

Solution: The position vector $\overrightarrow{OQ}$ of the particle will have the same coordinates as the point $Q$, because its starting point is at the coordinate origin, and it will be: $\overrightarrow{OQ} = -12i - 5j$.

Magnitude of the position vector is: $\left|\overrightarrow{OQ}\right| = \sqrt{(-12)^2 + (-5)^2} = \sqrt{(-12)^2 + (-5)^2} = \sqrt{169} = 13$.

And the unit vector along OQ will be: $\hat{u} = -\frac{12}{13} i - \frac{5}{13} j$.