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}=(P_2-P_1)/(|P_2-P_1|)\\\\\vec{D}=((-2i+3j+2k)-(i+2j+0))/(P_2-P_1)\\\\\vec{D}=(-3i+j+2k)/(√(3^2+1^2+2^2))\\\\\vec{D}=(-3i+j+2k)/(√(14))`

Now , mid point is given by :

`M((-2+1)/(2),(3+2)/(2),(2+0)/(2))\\\\M((-1)/(2),(5)/(2),1)`

Hence , this is the required solution .