Question

In a cartesian co-ordinate system, the co-ordinates of two points $P$ and $Q$ are $(2,4,4)$ and $(-2,-3,7)$ respectively. Find $\overrightarrow{PQ}$ and its magnitude.

Answer 1

$P=(2,4,4)$ and $Q=(-2,-3,7))$

$\overrightarrow{PQ}$= $(x_2-x_1)i$ $+(y_2-y_1)j$+ $(z_2-z_1)k$

$⟹\overrightarrow{PQ}=(-2-2)i+(-3-4)j+(7-4)k$

$⟹\overrightarrow{PQ}=-4i-7j+3k$

$|\overrightarrow{PQ}|=\sqrt{4^2+7^2+3^2}=\sqrt{74}$