A and B are expressed as A =2 i + j and B = i - j . Unit vector perpendicular to A and B is

Step-by-step solution

Given vectors are A = 2 i + j and B = i - j . A vector perpendicular to both A and B is given by their cross product A B . A B = (2 i + j ) ( i - j ) A B = 2( i i ) - 2( i j ) + ( j i ) - ( j j ) Since i i = 0 , j j = 0 , i j = k , and j i = - k : A B = 0 - 2 k - k - 0 = -3 k The magnitude of this vector is | A B | = |-3 k | = 3 . The unit vector perpendicular to both A and B is: n = A B | A B | = -3 k 3 = - k Answer: - k