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

In summary, there is no solution to the problem given. The problem might be mis-printed or copied incorrectly.
  • #1
Outrageous
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0

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
 
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  • #2
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
LCKurtz said:
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?
 
  • #4
Outrageous said:
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.
 
  • #5
The first way
 

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  • #6
Sorry a, my camera not good.
 
  • #7
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:
  • #8
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
Thanks
 
  • #10
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.
 
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  • #11
voko said:
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.
 

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

What is the difference between dot and cross product?

The dot product, also known as the scalar product, is a mathematical operation that results in a scalar quantity. It involves multiplying the magnitude of two vectors by the cosine of the angle between them. The cross product, also known as the vector product, is a mathematical operation that results in a vector quantity. It involves multiplying the magnitudes of two vectors by the sine of the angle between them.

How do I calculate the dot product?

To calculate the dot product of two vectors, you first multiply their corresponding components (x, y, and z) and then add the results. For example, if vector A = (2, 3, 5) and vector B = (4, 7, 1), the dot product AB = (2*4) + (3*7) + (5*1) = 8 + 21 + 5 = 34.

What is the physical interpretation of the cross product?

The cross product of two vectors results in a vector that is perpendicular to both of the original vectors. This means that the cross product can be used to determine the direction of a third vector that is perpendicular to a plane formed by the first two vectors. It is often used in physics and engineering to calculate torque, angular momentum, and magnetic fields.

Can the dot product of two vectors be negative?

Yes, the dot product can be positive, negative, or zero. The sign of the dot product depends on the angle between the two vectors. If the angle is less than 90 degrees, the dot product will be positive. If the angle is greater than 90 degrees, the dot product will be negative. And if the angle is exactly 90 degrees, the dot product will be zero.

What is the geometric meaning of the cross product?

The cross product of two vectors results in a vector that is perpendicular to both of the original vectors. Its magnitude is equal to the product of the magnitudes of the two original vectors multiplied by the sine of the angle between them. The direction of the cross product follows the right-hand rule, where you curl your fingers from the first vector to the second vector and the direction your thumb points is the direction of the cross product vector.

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