Perpendicular vector using dot not cross product.

In summary, to find a vector C perpendicular to both vectors A and B, we can use the dot product property stating that the dot product of perpendicular vectors is equal to zero. By setting the dot products of A and B with C equal to zero, we can solve for the unknown components of C. However, since C can also be a scalar multiple of itself, we are free to choose one of its components.
  • #1
Alex1976
3
0

Homework Statement


I have 2 (3d)vectors A and B and I want to find a vector C perpendicular to both of them.
A = 3i-2j+4k
B = -2i+5j-2k
C = Cx+Cy+Cz

Homework Equations


So we know A dot C = 3Cx-2Cy+4Cz and B dot C = -2Cx+5Cy-2Cz

The Attempt at a Solution

 
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  • #2
The dot product of perpendicular vectors is equal to zero. Use this to find vector C.

ehild
 
  • #3
edit...
 
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  • #4
Alex1976 said:
Yup I know that so we have:
A dot C = 0 = 3Cx-2Cy+4Cz
B dot C = 0 = -2Cx+5Cy-2Cz
But then I'm stuck.
I can isolate any of these obviously but I can't see how there's enough information for me to solve for my unknowns...

If [tex]\vec{C}[/tex] is perpendicular to [tex]\vec{A}[/tex] and to [tex]\vec{B}\,,[/tex] then so is [tex]k\,\vec{C}[/tex], where k is a scalar, so in general you will be free to choose one of the components of [tex]\vec{C}\,.[/tex]
 
  • #5
Wait. I see it now, thank's all.
 
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1. What is a perpendicular vector?

A perpendicular vector is a vector that forms a 90 degree angle (or right angle) with another vector.

2. How do you calculate the perpendicular vector using dot product?

The perpendicular vector can be calculated using the dot product by first finding the cross product between the two given vectors, and then taking the cross product of that result with one of the original vectors.

3. Can you use the cross product to find the perpendicular vector?

No, the cross product cannot be used to find the perpendicular vector. The cross product gives a vector that is perpendicular to both of the original vectors, not just one.

4. Why is the dot product used to find the perpendicular vector?

The dot product is used because it gives a scalar value (a number) that represents the length of the projection of one vector onto the other. When the dot product is zero, it means that the two vectors are perpendicular. This can be used to find the perpendicular vector by using the cross product method mentioned earlier.

5. Can you find the perpendicular vector using only one given vector?

No, you need at least two vectors to find the perpendicular vector. One vector alone does not have enough information to determine a perpendicular vector.

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