If b → = 2 i ^ - j ^ - k ^ , a → = 3 i ^ + 4 j ^ - 5 k ^ and b → × ( a → × b → ) = a → - k b → l then k l | b → | is

Question

If b → = 2 i ^ - j ^ - k ^ , a → = 3 i ^ + 4 j ^ - 5 k ^ and b → × ( a → × b → ) = a → - k b → l then k l | b → | is, the orthogonal projection of b → on a → and equal to 7 50, the orthogonal projection of a → on b → and equal to 7 6, the orthogonal projection of b → in the direction perpendicular to a → and equal to 5 3, the orthogonal projection of a → in the direction perpendicular to b → and equal to 752 3

MARKS App · Accepted Answer

Given, b → = 2 i ^ - j ^ - k ^ and a → = 3 i ^ + 4 j ^ - 5 k ^ So, b → × a → × b → = b → · b → a → - b → · a → b → = 6 a → - 7 b → = a → - 7 6 b → 1 6 . . . 1 As given, b → × ( a → × b → ) = a → - k b → l Comparing with 1 we get, l = 1 6 , k = 7 6 So, k l b → = 7 6 1 6 × 6 = 7 6

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