Question

The cross product produces a vector perpendicular to two other vectors if I remember correctly. My question is, do the original two vectors have to be perpendicular to each other before you cross them to get the 3rd perpendicular vector?

Answer 1

No.

Answer 2

Then what does the cross product do? Just creates a new vector?

Answer 3

Yes.

Answer 4

but the new vector is perpendicular to something i believe

Answer 5

To the two original vectors, the plane containing them http://bethycotter.wdfiles.com/local--files/vector-maths/Screen%20Shot%202014-08-13%20at%202.41.56%20PM.png

Answer 6

Let u and v be two vectors

Vector u and vector v do not have to be perpendicular to each other

u cross v = w is a new vector

u and w will be perpendicular (aka orthogonal)
v and w will be perpendicular (aka orthogonal)

Answer 7

so if i have two vectors that are NOT perpendicular and I cross them, what is the new vector? Is it perpendicular to anythin?

Answer 8

See above.

Answer 9

Or see your own post "The cross product produces a vector perpendicular to two other vectors"

Answer 10

so its perpendicular to the plane if the original vectors are not perpendicular to each other

Answer 11

and if the two vectors are perpendicular to each other then the cross product will create a 3rd perpendicular. vector.

Answer 12

It's perpendicular to both the original vectors, regardless. Angle between the original vectors is entirely irrelevant.

Answer 13

so the cross product will be perpendicular to both original vectors even if the original vectors are not perpendicular to each other?

Answer 14

Yes...

Answer 15

mind blown....

Answer 16

btw, notice if the two vectors are parallel, then the cross product is 0

if we "moved" both vectors so their tails are at the origin, both vectors would point in the same direction and "overlap" each other.

In that case, there are lots of planes that contain both vectors.... so we can't get a unique vector perpendicular to both original vectors.