Given the vectors u rightarrow = 4i + 3j - 3k, v rightarrow = -8i - 6j +6k, find

Question

Given the vectors u rightarrow = 4i + 3j - 3k, v rightarrow = -8i - 6j +6k, find the following cross and dot products. Determine whether it is orthogonal to both u rightarrow and v rightarrow. Show your work for ea. case. U rightarrow times v rightarrow = ______________________________(write your answer in standard vector form) u rightarrow. (u rightarrow times v rightarrow) = _______________________ v rightarrow. (u rightarrow times v rightarrow) = ________________________ Is the cross product orthogonal to u rightarrow and v rightarrow)?_______________________

Explanation / Answer

Answer is solved as below:

u cross v = (4i +3j-3k) cross (-8i-6j+6k) = -24k -24j +24k +18i+24j-18i=0

A cross product of 0 means u and v are parallel.

u X v = 0i+0j+0k

Since,u X v = 0i+0j+0k,
u.(u X v) = 0i+0j+0k
v.(u X v) = = 0i+0j+0k

Is the cross product orth. to u and v?

YES. we take the dpt product of either of u or v vector with (u cross v). If its 0 ( which is it in our case as u cross v itself is 0 proved above), then
answer to this question is YES

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