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JEE Main20266 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S . Then the square of the area of the parallelogram PQRS is __________.

Correct answer

0

Step-by-step solution

Let M₁ be the foot of the perpendicular from P(0, -5, 0) to the first line L₁: x-1 2 = y 1 = z+1 -2 . A general point on L₁ is M₁(2 + 1, , -2 - 1) . The direction ratios of PM₁ are (2 + 1, + 5, -2 - 1) . Since PM₁ is perpendicular to L₁ , their dot product is zero: 2(2 + 1) + 1( + 5) - 2(-2 - 1) = 0 4 + 2 + + 5 + 4 + 2 = 0 9 + 9 = 0 = -1 Thus, M₁ is (-1, -1, 1) . Let M₂ be the foot of the perpendicular from Q (0, -1 2 , 0 ) to the second line L₂: x-1 -1 = y+9 4 = z+1 1 . A general point on L₂ is M₂(- + 1, 4 - 9, -

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