The equation of the plane through the point 2 hat(i) - hat(j) -4 hat(k) and parallel to the plane vec(r) * ( 4 h

### Question Asked by a Student from EXXAMM.com Team

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
A

vec(r) * ( 4 hat(i) -12hat(j) -3 hat(k) ) =0

B

vec(r) * ( 4 hat(i) -12hat(j) -3 hat(k) ) =16

C

vec(r) * ( 4 hat(i) -12hat(j) -3 hat(k) ) =24 

D

vec(r) * ( 4 hat(i) -12hat(j) -3 hat(k) ) =32 `

#### HINT

(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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