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JEE MainMathematicsThree Dimensional Geometry

Let the line L be the line of intersection of the planes x - 2y + 3 = 0 and 2y + z - 3 = 0 . If Q is the image of the point P(0, -1, 1) in the line L , then the square of the distance of Q from the origin is _________

Correct answer

14

Step-by-step solution

Let us find a general point on the line L . Let y = . From the equations of the planes, we can express x and z in terms of : x - 2 + 3 = 0 x = 2 - 3 2 + z - 3 = 0 z = -2 + 3 So, any point on the line L can be written as M(2 - 3, , -2 + 3) . The direction ratios of the line L are proportional to the coefficients of , which are (2, 1, -2) . Let M be the foot of the perpendicular from P(0, -1, 1) to the line L . The direction ratios of PM are: (2 - 3 - 0, - (-1), -2 + 3 - 1) = (2 - 3, + 1, -2 + 2) Since PM is perpendi

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