JEE Main 2022 Mathematics question

If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a > 0 makes an angle 30° with the plane y − z + 2 = 0, then the direction cosines of the line are :

(1), , 0
(2), , 0Correct
(3), , 0
(4)1/2, , 0

Answer: (2)

Solution

The normals of the planes are , b, 0) and , b, c), so the direction of the line of intersection is , −ac, 0). The normal of the plane y − z + 2 = 0 is (0, 1, −1). The angle between the line and the

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Question ID VK-034340