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JEE Advanced Mathematics question

MathematicsThree Dimensional GeometryJEE Advanced

is a point on the – plane, making equal angles with the -axis and -axis and at a distance 2 from the origin. is the foot of the perpendicular from to the plane . The coordinates of are

Answer: (D)

Solution

lies in the -plane at to both axes, and . So

P=(0,\ 245°,\ 245°)=(0,Missing argument for \sqrt\sqrt2,Missing argument for \sqrt\sqrt2).

The foot is . Substituting into the plane:

9t+Missing argument for \sqrt\sqrt2+t-2+2t=2Missing argument for \sqrt\sqrt2\ ⇒\ 12t=2+Missing argument for \sqrt\sqrt2\ ⇒\ t=.

M=(

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Question ID VK-109866