How do I show these two vectors to be orthogonal and find a third vector to both of them?

I'm taking this engineering class right now and my hw assignment is essentially focused on vectors, which I'm trying to get a hang of. The question is:





Show that A=2i-j+4k %26amp; B=5i+2j-2k are orthogonal. Find a third vector that is perpendicular to both of these two vectors.





I'm still trying to get the hang of vectors and I would appreciate some help on this problem. If you could tell me the steps you took to solve this problem, I'd appreciate that as well.|||Vectors are NOT easy


remember 3 is a number, and "x" is an unknown number





(x,y) is a pair of numbers plotted on an area X _ Y plane but the (..) is one point





BUT ( Vector) (x,y) is one line (..) the ( ) is one number composed of the parts inside





complex number ( a + ib) is ONE complex vector like number





the unit vectors in two space are i = ( 1,0) and j = ( 0,1)





in three space i= ( x, 0, 0); j = ( 0,1,0) and k = ( 0,0,1)





Higher dimensions can be defined as ( x,y,z,s,t,u ...)





addition is addition of components but


Multiplication is NOT that simple





vector multiplication is DOT product, or Cross Product in 3 space and there is even a Cross Dot


but not a DOT CROSS





division is the devils own magic





study the definitions very very carefully





Vector math is very powerful in science especially physics but is NOT "common sense"





Orthogonal is A Dot B = 0





perpendicular is A Cross B