Question

I am asked to prove that the cross product of two vectors is orthogonal to both vectors. Does that just mean that the cross product is not zero?

Answer 1

yeah not zero cause i think when you multiply you should get a line that bisects the 2 lines at the diagonal: like if x is going in the north direction and y in the east directions when multiplied you get a vector lets say z going in the north east direction ... i think

Answer 2

Yes the cross product is perpendicular (or orthogonal) I just dont know the proof for this, just that it "is".

Answer 3

Im thinking that the proof is just that as long as its not zero then it must be orthogonal, im just not sure

Answer 4

....just multiply the vectors? or equations for the separate lines then the resulting equation should be the orthogonal line equation

Answer 5

?? that should work right

Answer 6

You can create 2 3D vectors, say v1 and v2, find the cross product of them, v3, then prove that the dot product of v3 with respect to both v1 and v2 is 0, since any two vectors with dot product = 0 are orthogonal

Answer 7

Yes, but the question is to prove that it is orthogonal. I guess I could do it like this. If the two vectors are and and b then the cross product is vector c. If I take the unit vectors of a and c then the dot product of a and c should be zero?

Answer 8

ah, yes, just what I was getting too. Thank you!