What is the cross-product of two vectors?
A vector orthogonal to both of them...
The cross product of two vectors in
We write the cross product of
#vec(u) xx vec(v) = < u_2v_3-u_3v_2, color(white)(.)u_3v_1-u_1v_2, color(white)(.)u_1v_2-u_2v_1 >#
If the angle between the vectors
#abs(abs(vec(u) xx vec(v))) = abs(abs(vec(u))) * abs(abs(vec(v))) color(white)(.)sin theta#
Another way of writing the cross product is:
#(u_1hat(i) + u_2hat(j) + u_3hat(k)) xx (v_1hat(i)+v_2hat(j)+v_3hat(k)) = abs((hat(i), hat(j), hat(k)), (u_1, u_2, u_3), (v_1, v_2, v_3))#
Note that if
See also https://socratic.org/s/aPeBh7vZ