If the magnitude of the projection of the vector i ^ - j ^ + 2 k ^ on the vector perpendicular to the plane containing the vectors 2 i ^ - j ^ + 3 k ^ and i ^ + j ^ - 2 k ^ is k , then the value of 1 k 2 is equal to

Question

If the magnitude of the projection of the vector i ^ - j ^ + 2 k ^ on the vector perpendicular to the plane containing the vectors 2 i ^ - j ^ + 3 k ^ and i ^ + j ^ - 2 k ^ is k , then the value of 1 k 2 is equal to,

MARKS App · Accepted Answer

A vector perpendicular to the plane is i ^ j ^ k ^ 2 - 1 3 1 1 - 2 = i ^ - 1 - j ^ - 7 + k ^ 3 = - i ^ + 7 j ^ + 3 k ^ = b → l e t Let, a → = i ^ - j ^ + 2 k ^ Projection of a → on b → = a → ⋅ b → b → = - 1 - 7 + 6 59 = 2 59 = k

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