Any Vector A is given by A = xi + yj. The another vector B perpendicular to A can be written as

Using the concept of dot product of two vectors.
A. B = AB cos θwhere θ is the angle between the two vectorsgiven, A = xi^ + yj^when two vectors are perpendicular to each other, the angle (θ) between them is 900 and cos 900 = 0
and A. B = AB cos 900 = 0it means that the dot product of 2 perpendicular vectors is zero.for unit vectors,i ^. j^ = j^. k^ = k ^. i^ =0hence, vector B can be equal to xj^  + yk^

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