If V ¯ = 2 i ¯ + j ¯ - k ¯ , W ¯ = i ¯ + 3 k ¯ and U ¯ is a unit vector, then the maximum value of [ U ¯ V ¯ W ¯ ] is

Step-by-step solution

It is given that, V → = 2 i ^ + j ^ - k ^ W → = i → + 3 k ^ The cross product is, V → × W → = i ^ j ^ k ^ 2 1 - 1 1 0 3 = i ^ 3 - 0 - j ^ 6 + 1 + k ^ 0 - 1 = 3 i ^ - 7 j ^ - k ^ Therefore, [ U → V → W → ] = U · ( V → × W → ) = | U → | | V → × W → | cos θ = ( 1 ) ( 9 + 49 + 1 ) cosθ = 1 ( 59 ) cos θ The maximum value of [ U → V → W → ] is, [ U → V → W → ] = 59 cos 0 &#1