For the given vector x 3 1 2 find all the orthogonal on the

For the given vector x = [3 1 -2]. find all the orthogonal on the following candidates

Solution

x = [ 3, 1, -2]

Orthogonal vector A to x would: Dot product of A and x

A.x =0

A.x = (3, 1, -2).( x1. x2 , x3)

Check all vectors : x1.x = ( 0, 4 , 2)( 3, 1, -2) = 0 +4 -4 =0

x2.x = ( -1, -1, -2)( 3, 1, -2) = -3 -1 +4 =0

x3.x = ( -3, -1, 2)(3, 1, -2) = -9-1-4 not equal to zero

x4.x = (0.5, -1 , 0.25)( 3 , 1 -2) =1.5, -1 , -0.5 =0

So, x1 , x2 and x4 are orthogonal to x vectors