I have been give the following problem: the vector perpendicular to OA and OB where O, B, A are points with respective coordinates of (0,0,0), (-4,2,1) and (1,2,3) is of the form 4i+yj+zk. What are the values of y and z?
How do i go about working this out???
As suggested take the cross product of OA and OB which will yield a vector perpendicular to both vectors. You are told that there is a vector of the form (4,y,z) that is also perpendicular to both OA and OB. So, (4,y,z) is some scalar multiple of the cross product between OA and OB:
(leaving it up to you to find the cross product i.e. what a, b, and c are)
So, (a, b, c) = k(4, y, z).
Looking at the x component, you can see that a = 4k. Solve for k, then you should be able to find y and z (b = ky; c = kz).