Let a line pass through two distinct points P(-2,-1,3) and Q , and be parallel to the vector 3 i +2 j +2 k . If the distance of the point Q from the point R (1,3,3) is 5 , then the square of the area of P Q R is equal to :

Step-by-step solution

Equation of line P Q is: x+2 3 = y+1 2 = z-3 2 =r( say ) Let coordinate of Q=(3 r-2,2 r-1,2 r+3) P R=5 Then aligned & (3 r-2-1)^2+(2 r-1-3)^2+(2 r+3-3)^2=25 & r=0 or 2 & Coordinate of Q=(4,3,7) aligned aligned & square of area of P Q R= | 1 2 ( P Q P R ) |^2 & = | 1 2 (6 i +4 j +4 k ) (3 i +4 j ) |^2 & =|-8 i +6 j +6 k |^2=136 aligned