Question

For the points P1(-2,3,2) and P2(1,2,0) ​, find the direction of P1P2 and the midpoint of line segment P1P2.

Answer 1

Given :

Two points $P_1(-2,3,2)\ and\ P_2(1,2,0)$ .

To Find :

The direction of $P_1P_2$ and midpoint of line segment $P_1P_2$ .  

Solution :

Direction of $P_1$ and $P_2$ is given by :

$\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}$

Now , mid point is given by :

$M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)$

Hence , this is the required solution .