Let a = 2 i - 3 j + k , b = 3 i + 2 j + 2 k , c = 4 i - 3 j + k , then the vectors a , b , c are

Step-by-step solution

The vectors are a = 2 i - 3 j + k , b = 3 i + 2 j + 2 k , and c = 4 i - 3 j + k . To check for linear independence, we evaluate the scalar triple product [ a b c ] which is given by the determinant of their components: [ a b c ] = vmatrix 2 & -3 & 1 3 & 2 & 2 4 & -3 & 1 vmatrix Applying the row operation R₃ R₃ - R₁ : [ a b c ] = vmatrix 2 & -3 & 1 3 & 2 & 2 2 & 0 & 0 vmatrix Expanding along the third row: [ a b c ] = 2((-3)(2) - (1)(2)) = 2(-6 - 2) = -16 Since [ a b c ] 0 , the vectors are non-coplanar and hence li