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

Step-by-step solution

Given vectors a & b are unit vectors. array l Now (2 a - b ) [( a b ) ( a +2 b )] =-(2 a - b ) [( a +2 b ) ( a b )] =-(2 a - b ) [ a ( a b )+2 b ( a b )] =-(2 a - b )[( a b ) a -( a a ) b +2( b b ) a -2( b a ) b ] =-(2 a - b )[( a b ) a - b +2 a -2( b a ) b ] Here a b = 3(2) 7 10 - 1(6) 7 10 =0 array Hence given expression becomes array l =-(2 a - b )[- b +2 a ]=-(2 a - b )² =- [4 a ²+ b ²-4 a b ]=-(4+1)=-5 array