If the vectors a =2 i -3 j +4 k ; b = i +2 j - k and c =m i - j +2 k are coplanar, then the value of m is

Step-by-step solution

Three vectors a , b , and c are coplanar if and only if their scalar triple product is zero, which is given by the determinant of the matrix formed by their components. The condition is a ( b c ) = 0 , which implies: vmatrix 2 & -3 & 4 1 & 2 & -1 m & -1 & 2 vmatrix = 0 Expanding the determinant along the first row: 2(2 2 - (-1) (-1)) - (-3)(1 2 - (-1) m) + 4(1 (-1) - 2 m) = 0 2(4 - 1) + 3(2 + m) + 4(-1 - 2m) = 0 2(3) + 6 + 3m - 4 - 8m = 0 6 + 6 + 3m - 4 - 8m = 0 8 - 5m = 0 5m = 8 m = 8 5 Answer: 8 5