# Cross product of vectors.

• February 23rd 2011, 04:54 PM
Rumor
Cross product of vectors.
Here's the problem: "Given that v = 2i + 3j - k and w = i - j + 2k, find (v x w) x w."

For some reason, I can't seem to get the right answer for this question.

v x w = [2, 3, -1] x [1, -1, 2] = (6-1)i + (4-(-1))j + (-2-3)k = 5i + 5j -5k

Then, (v x w) x w = [5, 5, -5] x [1, -1, 2] = (10-5)i + (10-(-5))j + (-5-5)k = 5i + 15j - 10k.

Could someone tell me where I went wrong?
• February 23rd 2011, 05:01 PM
dwsmith
Quote:

Originally Posted by Rumor
Here's the problem: "Given that v = 2i + 3j - k and w = i - j + 2k, find (v x w) x w."

For some reason, I can't seem to get the right answer for this question.

v x w = [2, 3, -1] x [1, -1, 2] = (6-1)i + (4-(-1))j + (-2-3)k = 5i + 5j -5k

Then, (v x w) x w = [5, 5, -5] x [1, -1, 2] = (10-5)i + (10-(-5))j + (-5-5)k = 5i + 15j - 10k.

Could someone tell me where I went wrong?

Looks fine.
• February 23rd 2011, 05:07 PM
Rumor
Hm... Okay. Maybe I'm just misinterpreting the question, then. The exact wording of the problems tells me to "calculate the given quantity." Is that not what I did? Or is it looking for an actual number?
• February 23rd 2011, 05:09 PM
dwsmith
Quote:

Originally Posted by Rumor
Hm... Okay. Maybe I'm just misinterpreting the question, then. The exact wording of the problems tells me to "calculate the given quantity." Is that not what I did? Or is it looking for an actual number?

The cross product is a vector normal to the vectors. Should it be $(v\times w)\cdot w\text{?}$
• February 23rd 2011, 05:17 PM
Rumor
Quote:

Originally Posted by dwsmith
The cross product is a vector normal to the vectors. Should it be $(v\times w)\cdot w\text{?}$

No, the notation is given as (v x w) x w.