Vector component of a orthogonal to b

[jman2807]

The question asks to find the vector component of a that is orthogonal to vector b.
a = <1,1,2> b = <2,-1,2>

I know that means that the dot product of the new vector you must find and b must = 0 for them be orthogonal, but i dont know how to find it as a component of a. Any help is appreciated. Thanks in advance.

 

[daon]

You can find the projection of a onto b, right? Let P be that projection. Then all you need to do is subtract P from a.

(sorry for the quality, I used paint)

 

[jman2807]

Ah, now i understand. Thank you.