Find the equation of the plane passing through the point `(-1,2,1)` and perpendicular to the line joining the points `(-3,1,2)a n d(2,3,4)dot` Find also the perpendicular distance of the origin from this plane.

Explanation

Direction ratios of line joining points `(-3,1,2)` and `(2,3,4)`
are `(2+3,3-1,4-2)` i.e `(5,2,2). `

∴ Required equation of plane passing through the point
`(-1,2,1)` and n having normal with direction ratio `(5,2,2)` is

`a(x−x1)+b(y−y1)+c(z−z1)=0`

`⇒5(x+1)+2(y−2)+2(z−1)=0`

`⇒5x+5+2y−4+2z−2=0`

`⇒5x+2y+2z−1=0`

`⇒r⋅(5i+2j+2k)−1=0`