How do you find a unit vector b perpendicular to another unit normal vector?

How do you find a unit vector b perpendicular to another unit normal vector, which is (4/5)i + (2/5)j - (3/5) k





your help would be much appreciated!





Thank you!|||Call our original unit vector u. Call our resulting perpendicular unit vector b.





Set v equal to a cross product of u and another arbitrary unit vector:


b = u ×%26lt;1, 0, 0%26gt;





Remember the cross product will always return a vector perpendicular to both original vectors.





u ×%26lt;1, 0, 0%26gt; =


| î ... ĵ ... ĸ ..|


| ux . uy . uz|


| 1 ... 0 ... 0 |





=


%26lt;0, uz, -uy%26gt;





=


%26lt;0, -3/5, -2/5%26gt;





And then be sure to normalize its magnitude:


%26lt;0, -3/5, -2/5%26gt;/sqrt((3/5)^2 + (2/5)^2) = %26lt;0, 3/5, -2/5%26gt;*5/sqrt(13)





Result:


b = %26lt;0, -3/sqrt(13), -2/sqrt(13)%26gt;