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A tetrahedron has vertices at $O (0, 0, 0) A (1, 2, 1), B (2, 1, 3)$ and $C (- 1, 1, 2)$ , then the angle between faces OAB and ABC will be

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30 ∘

cos − 1 1731

cos − 1 1935

90 ∘

answer is A.

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Detailed Solution

n 1 ¯ = O A × O B = i j k 121213 = 5 i − j − 3 k

n 2 → = A B × A C = 1 j κ 1 − 1 2 − 2 − 1 1 = i − 5 j − 3 k

θ = cos − 1 n 1 → n 2 → n 1 → n 2 → = cos − 1 1935

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