Dot and cross product?

1. Aug 11, 2013

Outrageous

1. The problem statement, all variables and given/known data
A=(x,3,1) ,B=(x,-x,2)
Determine the value of x if the vector perpendicular to A and B is given by C=(10,-4,-4)

2. Relevant equations

3. The attempt at a solution
Find A cross B , let A cross B be D . Then D cross C = zero (since they are perpendicular to both A and B) . This sounds logic but there will not be an answer for x. What is wrong?
Then I tried to use dot product A dot C=0, and B dot C=0. Yet the answer of two x are different.

2. Aug 11, 2013

LCKurtz

You haven't shown your calculations. But perhaps there is no real value of x that works. Perhaps the problem is mis-printed or copied incorrectly.

3. Aug 11, 2013

Outrageous

So the both ways to solve the problem are correct?

4. Aug 11, 2013

LCKurtz

I didn't say that. I haven't worked the problem; that's your job. If you want me to comment on what you did you need to show your work.

5. Aug 11, 2013

Outrageous

The first way

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6. Aug 11, 2013

Outrageous

Sorry a, my camera not good.

7. Aug 11, 2013

Outrageous

Please look at the picture, I don't know why I can't upload more picture.
The second way, A dot C = 0 , x= 1.6
B dot C = 0 , x= 0.4
Thanks

Last edited: Aug 11, 2013
8. Aug 11, 2013

LCKurtz

I won't try to read upside down. But if your arithmetic is correct and you get different values for $x$, that would tell you there is no solution. Like I said earlier, perhaps the problem is mis-printed or copied incorrectly.

9. Aug 11, 2013

Outrageous

Thanks

10. Aug 12, 2013

voko

I would like to remark that your approach with the cross product is over-complicated. Once you found C = A x B, and assume that C is parallel with D, you can say C = k D, where k is some number. You do not need to cross-multiply C and D, you just need to confirm that C = k D is possible.

11. Aug 12, 2013

Outrageous

Really easier. But I think the question have some problems. Thank you.