Let A → be a vector parallel to the line of intersection of the planes P 1 and P 2 . The plane P 1 is parallel to the vectors 2 j ^ + 3 k ^ and 4 j ^ - 3 k ^ while plane P 2 is parallel to the vectors j ^ - k ^ and i ^ + j ^ . The acute angle between A → and 2 i ^ + j ^ - 2 k ^ is

Question

Let A → be a vector parallel to the line of intersection of the planes P 1 and P 2 . The plane P 1 is parallel to the vectors 2 j ^ + 3 k ^ and 4 j ^ - 3 k ^ while plane P 2 is parallel to the vectors j ^ - k ^ and i ^ + j ^ . The acute angle between A → and 2 i ^ + j ^ - 2 k ^ is, π 6, π 4, π 3, 5 π 12

MARKS App · Accepted Answer

Let, a → = 2 j ^ + 3 k ^ b → = 4 j ^ - 3 k ^ c → = j ^ - k ^ d → = i ^ + j ^ e → = 2 i ^ + j ^ - 2 k ^ A normal vector perpendicular to the plane P 1 is a → × b → A normal vector perpendicular to the plane P 2 is c → × d → A vector parallel to the line of intersection is a → × b → × c → × d → = k ^ - j ^ Let, θ be the acute angle between them then, cos ⁡ θ = A → · e → A → e → = - 3 2 × 3 = 1 2 ⇒ θ = π 4

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