Calculating x for Perpendicular Vectors A and B: Dot and Cross Product Homework

[Outrageous]

Homework Statement

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)

Homework Equations

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.
Please guide. Thanks

 

[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.

 

[Outrageous]

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.

So the both ways to solve the problem are correct?

 

[LCKurtz]

So the both ways to solve the problem are correct?

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.

 

[Outrageous]

The first way

 

[Outrageous]

Sorry a, my camera not good.

 

[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

 

[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.

 

[Outrageous]

Thanks

 

[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.

 

[Outrageous]

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.

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