Question

Suppose the first vector pointed to the right of the page, and the second vector pointed up toward the top of the page. Which direction would the cross product of these two vectors point?

Answer 1

Suppose x-direction is in the right of the page, y-direction in pointed upward of the page and z-direction is out of the page, then

R1 = towards the right of the page = (R1) i

R2 = towards the top of the page = (R2) j

So, their cross-product will be:

R1xR2 = (R1 i)x(R2 j)

R1xR2 = R1*R2*(ixj)

ixj in cross-product is +k, So

R1xR2 = R1*R2 (k)

So direction of cross product will be out of the page

Or use right hand rule:

If you point your thumb in right-hand direction and fingers in the upward direction, then direction of palm will be direction of cross-product, So in this case your palm is out of the page, So

Direction = Out of the page (+k)

Let me know if you've any query.