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Hi, here's my question:Find the vector, not with determinants, but by using properties of cross products.(i + j) x (i - j)My prof didn't cover these types of problems very well in class, so a detailed solution will help. Thanks!

Question

Hi, here's my question:

Find the vector, not with determinants, but by using properties of cross products.

(ij) x (ij)

My prof didn't cover these types of problems very well in class, so a detailed solution will help. Thanks!

check_circleAnswer
Step 1

 We know that,

i xi= 0
i xj k
jxi-k
jxj 0
j xk i
k xj-i
k x k
0
kxi j
ixk -j
help_outline

Image Transcriptionclose

i xi= 0 i xj k jxi-k jxj 0 j xk i k xj-i k x k 0 kxi j ixk -j

fullscreen
Step 2

Calculati...

x (i - j)
(i
= ixi- ixj+jxi-jxj
=0 k - k - 0
= -2k
help_outline

Image Transcriptionclose

x (i - j) (i = ixi- ixj+jxi-jxj =0 k - k - 0 = -2k

fullscreen

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