Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).
Calculate the following, expressing your answers as ordered triples (three comma-separated numbers). B⃗ ×C⃗

Question

anonymous · Answer

http://en.wikipedia.org/wiki/Cross_product

owlfred · Answer

Do you know the general expression for a cross product in terms of components? It's a simple 3x3 determinant.

mony01 · Answer

oh do i need to find the determinant?

owlfred · Answer

Yes, you need to evaluate the determinant. If you don't know what they are, never really mind - it's just another overwhelming word that is truly simple. 

In general, if $\vec A = (x_1, y_1, z_1)$ and $\vec B = (x_2, y_2, z_2)$, then...
 $\vec A \times \vec B = \hat i (y_1 z_2 - y_2 z_1) - \hat j (x_1 z_2 - x_2z_1) + \hat k (x_1 y_2 - x_2 y_1)$

owlfred · Answer

In your notation, it is $(y_1 z_2 - y_2 z_1 , ~x_2 z_1 - x_1 z_2, ~x_1 y_2 - x_2 y _ 1) $

mony01 · Answer

what if it was to find A⃗ ×(B⃗ ×C⃗ )

owlfred · Answer

Then you would first find $\vec B \times\vec C$, then cross that with $\vec A$. Careful, though, with the order - cross product is not commutative.

mony01 · Answer

so BxC=(4,5,-17) and A=(1,0,-3) so i do the same thing as above

parthkohli · Answer

Yes.

mony01 · Answer

thanks

parthkohli · Answer

No problem!