Question

Find the vector between 𝑂(−5, 2, 3) and 𝑃(3, 0, −4) in Cartesian form and calculate the magnitude of the vector. 

Answer 1

Let OP be the vector between O(-5,2,3) and P(3,0,-4). Therefore,

OP=$(3 - -5) \vec{i}+(0 - 2)\vec{j}+(-4 - 3)\vec{k}=8\vec{i}-2\vec{j}-7\vec{k}$

Magnitude of OP is denoted by |OP|, where

|OP| = $\sqrt{(8)^2+(-2)^2+(-7)^2}$ = $\sqrt{117}=10.8167$ units