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MathematicsSingle correct+4 / -1Question 17 of 90

JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 17

Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S:x+y+z=5S:x+y+z=5. If a line L passing through (1,−1,−1)(1,-1,-1), parallel to the line PQ meets the plane S at R, then QR2QR^2 is equal to :

Choose one option
Answer and worked solution

Official answer: B

Image of P. Foot of the perpendicular: t=5−23=1t=\dfrac{5-2}3=1, foot (2,1,2)(2,1,2), so Q=(3,2,3)Q=(3,2,3).

Point R. L is (1+t,−1+t,−1+t)(1+t,-1+t,-1+t); on S: −1+3t=5-1+3t=5, t=2t=2, R=(3,1,1)R=(3,1,1).

Distance. QR2=0+1+4=5QR^2=0+1+4=5.

(B)

Topics:Equation of a planeEquation of a line in space
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