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JEE Main202226 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

The largest value of a , for which the perpendicular distance of the plane containing the lines r → = i ^ + j ^ + λ i ^ + a j ^ - k ^ and r → = i ^ + j ^ + μ - i ^ + j ^ - a k from the point 2 , 1 , 4 is 3 , is ______.

Correct answer

0

Step-by-step solution

Given, r → = i ^ + j ^ + λ i ^ + a j ^ - k ^ r → = i ^ + j ^ + μ - i ^ + j ^ - a k Direction ratio of plane containing these lines is given by, i ^ j ^ k ^ 1 a - 1 - 1 1 - a = i ^ 1 - a 2 - j ^ - a - 1 + k ^ 1 + a n → = 1 - a i ^ + j ^ + k ^ Also plane is passing through the point 1 , 1 , 0 So, equation of plane will be, 1 - a x - 1 + y - 1 + z - 0 = 0 1 - a   x + y + z + a - 2 = 0 Now distance of point 2 , 1 , 4 from this plane is 3 ∴   D = 1 - a 2 + 1 + 4 + a - 2 1 - a

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