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.

Options

A. `r*(5hati+2hatj+2hatk)=1`
B. `r*(5hati+2hatj+2hatk)=-1`
C. `r*(5hati-2hatj+2hatk)=-5`
D. `r*(5hati-2hatj-2hatk)=1`

Answer

A

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). Since, plane is perpendicular to the line joining the given points therefore direction ratio of normal to the plane are (5,2,2)
`therefore` Required equation of plane passing through the point (-1,2,1) andn having normal with direction ratio (5,2,2) is
`a(x-x_(1))+b(y-y_(1))+c(z-z_(1))=0`
`implies5(x+1)+2(y-2)+2(z-1)=0`
`implies5x+5+2y-4+2z-2=0`
`implies5x+2y+2z-1=0`
`impliesr*(5hati+2hatj+2hatk)-1=0`