If a = 1 10 (3 i + k ) and b = 1 7 (2 i +3 j -6 k ) then the value of (2 a - b ) [( a b ) ( a +2 b )]=

Step-by-step solution

Given vectors a = 1 10 (3 i + k ) and b = 1 7 (2 i + 3 j - 6 k ) , both have unit magnitude since | a | = 1 and | b | = 1 . Their dot product a b = 0 , confirming orthogonality. The expression (2 a - b ) [( a b ) ( a + 2 b )] simplifies using the vector triple product identity. For orthogonal unit vectors, ( a b ) a = b and ( a b ) b = - a , yielding ( a b ) ( a + 2 b ) = b - 2 a . The dot product becomes (2 a - b ) ( b - 2 a ) = -|2 a - b |^2 . Since |2 a - b |^2 = 4| a |^2 - 4( a b ) + | b |^2 = 4 + 0 + 1 = 5 , t