If the axes are rectangular and `P` is the point (2, 3, -1), find the equation of the plane through `P` at right angle to `O Pdot`

Options

A. `2x+3y+z=16`
B. `2x+3y-z=14`
C. `2x+3y+z=14`
D. `2x+3y-z=0`

Answer

B

Explanation

Since, coordinates of point O and P are (0,0,0) and (2,3,-1) respectively.
Direction ratio of OP are lt2,3,-1gt
The plane is perpendicular to OP. So, its equation is
`2x+3y-z+d=0`
Since, this plane passes through `(2,3,-1),2xx2+3xx3-1xx-1+d=0`
`rArr 4+9+1d=0`
`rArr d=-14`
On putting the value of d in Eq.(i)
`2x+3y-z-14=0`
`rArr 2x+3y-z=14`
Which is required equation of plane.