The scalar components of a unit vector which is perpendicular to each of the vectors +2 - k and 3 - +2 k are

Step-by-step solution

Let a = i + 2 j - k and b = 3 i - j + 2 k . A vector perpendicular to both a and b is given by their cross product n = a b . n = vmatrix i & j & k 1 & 2 & -1 3 & -1 & 2 vmatrix n = i (2(2) - (-1)(-1)) - j (1(2) - (-1)(3)) + k (1(-1) - 2(3)) n = i (4 - 1) - j (2 + 3) + k (-1 - 6) n = 3 i - 5 j - 7 k The magnitude of n is | n | = 3^2 + (-5)^2 + (-7)^2 = 9 + 25 + 49 = 83 . The unit vector perpendicular to both a and b is n | n | = ( 3 83 i - 5 83 j - 7 83 k ) . Comparing this with the given options, the components are