1. 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?

2. 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.

3. 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?

4. 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 $(v\times w)\cdot w\text{?}$

5. 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.