Let A be the image of the point R(0, -1, 0) in the line L₁ : x-2 1 = y -1 = z-2 1 . Let L₂ be a line passing through A and perpendicular to both L₁ and the line L₃ : x-1 1 = y -1 = z-1 2 . If d is the shortest distance between L₂ and the z-

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Let A be the image of the point R(0, -1, 0) in the line L₁ : x-2 1 = y -1 = z-2 1 . Let L₂ be a line passing through A and perpendicular to both L₁ and the line L₃ : x-1 1 = y -1 = z-1 2 . If d is the shortest distance between L₂ and the z-axis, then the value of 2d^2 is equal to ________

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Let Q be the foot of the perpendicular from R(0, -1, 0) to L₁ . A general point on L₁ is Q( +2, - , +2) . The direction ratios of RQ are ( +2, - +1, +2) . Since RQ is perpendicular to L₁ , we have: 1( +2) - 1(- +1) + 1( +2) = 0 + 2 + - 1 + + 2 = 0 3 + 3 = 0 = -1 So, Q is (1, 1, 1) . Since Q is the midpoint of R and its image A , we have: A = 2Q - R = (2(1)-0, 2(1)-(-1), 2(1)-0) = (2, 3, 2) . The line L₂ is perpendicular to both L₁ and L₃ . Its direction vector b is given by the cross product of their direction vect

Let A be the image of the point R(0, -1, 0) in the line L₁ : x-2 1 = y -1 = z-2 1 . Let L₂ be a line passing through A and perpendicular to both L₁ and the line L₃ : x-1 1 = y -1 = z-1 2 . If d is the shortest distance between L₂ and the z-axis, then the value of 2d^2 is equal to ________

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