If x = b c [ a b c ] , y = c a [ a b c ] and z = a b [ a b c ] where a , b , c are non-coplanar vectors, then value of x ( a + b )+ y ( ~b + c )+ z ( c + a ) is

Step-by-step solution

aligned & x ( a + b )+ y ( ~b + c )+ z ( c + a ) = & ( a + b ) x +( b + c ) y +( c + a ) z & = [ a b c ]+0+[ b c a ]+0+[ c a b ]+0 [ a b c ] = & 3 aligned