If a = i - k , b = x i + j + (1-x) k and c = y i + x j + (1+x-y) k then [ a b c ] depends on

Step-by-step solution

The scalar triple product [ a b c ] is given by the determinant of the components of the vectors. [ a b c ] = vmatrix 1 & 0 & -1 x & 1 & 1-x y & x & 1+x-y vmatrix Applying the column operation C₃ C₃ + C₁ : [ a b c ] = vmatrix 1 & 0 & 0 x & 1 & 1 y & x & 1+x vmatrix Expanding the determinant along the first row: [ a b c ] = 1 (1(1+x) - 1(x)) [ a b c ] = 1 + x - x = 1 Thus, the scalar triple product is a constant and is independent of both x and y . Answer: neither x nor y