Let the plane P : r a = d contain the line of intersection of two planes r ( i + 3 j - k ) = 6 and r (-6 i + 5 j - k ) = 7. If the plane P passes through the point (2, 3, 1/2), then the value of |13 a |^ 2 /d^ 2 is equal to

JEE Main 2022 Mathematics question

Let the plane P : contain the line of intersection of two planes and . If the plane P passes through the point (2, 3, 1/2), then the value of is equal to

(1)90
(2)93Correct
(3)95
(4)97

Answer: (2)

Solution

The planes are x + 3y − z = 6 and −6x + 5y − z = 7. A plane through their line of intersection is . It passes through (2, 3, 1/2): , i.e. ,

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Question ID VK-034972