JEE Main202524 Jan 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the image of the point Q (7,-2,5) in the line L : x-1 2 = y+1 3 = z 4 and R (5, p , q ) be a point on L . Then the square of the area of P Q R is ________.

Correct answer

Step-by-step solution

aligned & Let R (2 +1,3 -1,4 ) & 2 +1=5 & =2 & R (5,5,8) & let T (2 +1,3 -1,4 ) & QT =(2 -6) i +(3 +1) j +(4 -5) k & b =2 i +3 j +4 k & QT b =0 & 4 -12+9 +3+16 -20=0 aligned aligned & =1 & ~T (3,2,4) & QT = 33 RT = 29 & ( area of PQR )^2= ( 1 2 29 2 33 )^2 & =957 aligned

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