If the angle between the plane x - 3 y + 2 z = 1 and the line x - 1 2 = y - 1 - 1 = z - 1 - 3 is θ , then sec ⁡ 2 θ is equal to

Question

If the angle between the plane x - 3 y + 2 z = 1 and the line x - 1 2 = y - 1 - 1 = z - 1 - 3 is θ , then sec ⁡ 2 θ is equal to, 107 11, 98 97, 100 9, 87 79

MARKS App · Accepted Answer

A normal vector to the plane n → = 1 , - 3 , 2 > A vector parallel to the line b → = 2 , - 1 , - 3 > sin θ = b → . n → b → ⋅ n → = 2 + 3 − 6 14 14 = − 1 14 sec ⁡ 2 θ = 1 cos ⁡ 2 θ = 1 1 - 2 s i n 2 θ = 1 1 - 2 196 = 196 194 = 98 97

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