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Q 2242145033.     Let `A` be the given point whose position vector relative to an origin `O` be a and `ON = n`. Let `r` be the position vector of any point
`P` which lies on the plane and passing through `A` and perpendicular to `ON`. Then for any point `P` on the plane.
` vec(AP) *vec(n) =0`
`=> ( vec(r) - vec(a) ) * vec(n)=0`
`=> vec(r) * vec(n) = vec(a) * vec(n)`
`=> vec(r) * vec(n) =p`
where `P` is perpendicular distance of the plane from origin.
The equation of the plane through the point `2 hat(i) - hat(j) -4 hat(k)` and parallel to the plane
`vec(r) * ( 4 hat(i) -12hat(j) -3 hat(k) ) -7 =0` is
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)