JEE Advanced Mathematics question

; ; are the direction cosines of three mutually perpendicular lines. The direction cosines of the line equally inclined to them are

(A)
(B)
(C)Correct
(D)

Answer: (C)

Solution

Take the unit vectors , . They are mutually perpendicular, so for and .

*(Figure: O at the top, with OA, OB, OC each of length 1 along the three perpendicular lines; A = (l₁, m₁, n₁), B = (l₂, m₂, n₂), C = (l₃, m₃, n₃); G is

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Question ID VK-109808