Why isn't the cross product working?

In summary, the problem is asking to find a unit vector with a positive first coordinate that is orthogonal to both vectors a = <1,2,1> and b = <1,8,1>. The suggested method is to take the cross product of the two vectors and then make sure the resultant vector is a unit vector. However, this method may not always result in a unit vector, so other operations may need to be performed to achieve the desired result. One suggestion is to multiply the vector by -1. It is also important to carefully read the problem and understand what type of vector is being asked for.
  • #1
mr_coffee
1,629
1
Hello everyone, this should be a simple problem..its for matrices and I already delt with this in calc III and physics but it says:
find a unit vector with positive first coordinate orthogonal to both a and b.
a = <1,2,1>
b = < 1,8,1>
so i took the cross product and got:
<-6,0,6> it says, my j component is right but the i and k are wrong. Any ideas why?
 
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  • #2
You are looking for a unit vector, check the definition of unit vector, you will see that your result does not conform. What do you need to do to make it fit the definition?
 
  • #3
ohh my bad, well i tried it 2 different ways and still got it wrong... a unit vector is when u take the mangitude of the vector and then multiply 1/magnitude to the orignal vector and that's your unit vector. So I thought maybe it wants me to find the unit vector of <1,2,1> & <1,8,1> so i found the unit vector of each of them, and then tookk the cross product of each unit vector and got a wrong answer, so then i thought maybe they just want me to find the unit vector of the resultant of <1,2,1> x <1,8,1> it was also wrong...any ideas?
 
  • #4
Your RESULT needs to be a unit vector. You do not necessarily get a unit vector as the result of operations on unit vectors. What can you do to make your resultant a unit vector. Also what operations can you to to get vector with the requested direction of the x component?
 
  • #5
Just a thought.. try multiplying the vector by -1. <6, 0, -6> is still orthogonal to both a and b.
 
  • #6
mr_coffee said:
so then i thought maybe they just want me to find the unit vector of the resultant of <1,2,1> x <1,8,1> it was also wrong...
This is what you want to do. So, what is the unit vector along (-6,0,6) ?

And once you find this vector, if it is not the required answer, check its negative as well (as suggested by hammie).
 
  • #7
I think the answer in all this is: "read the problem just a LITTLE more carefully".

Especially about what kind of vector to find.

Unit vector was only one requirement.
 

1. Why am I getting an error when trying to calculate the cross product?

There are a few common reasons for errors when calculating the cross product. One possibility is that the vectors being used are not of the same dimensionality. Another possibility is that the vectors are not perpendicular, which is a requirement for the cross product to be defined. Additionally, make sure that the vectors are in the correct order when inputting them into the cross product formula.

2. Why is my cross product resulting in a zero vector?

If the cross product is resulting in a zero vector, it means that the two input vectors are parallel to each other. This is because the cross product is only defined for non-parallel vectors, and the result of the cross product is a vector that is perpendicular to both input vectors.

3. Can I use the cross product with more than two vectors?

No, the cross product is only defined for two vectors at a time. It is not possible to use more than two vectors in a cross product calculation.

4. Does the order of the input vectors matter when calculating the cross product?

Yes, the order of the input vectors does matter when calculating the cross product. Switching the order of the vectors will result in a vector with the same magnitude but opposite direction.

5. What is the significance of the cross product in mathematics?

The cross product has many applications in mathematics, physics, and engineering. It is used to calculate the area of a parallelogram, determine the torque on an object, and find the normal vector to a plane. It is also used in vector calculus to calculate line integrals and surface integrals.

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