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Perpendicular vector using dot not cross product.

  • Thread starter Alex1976
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  • #1
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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

 
Last edited:

Answers and Replies

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

ehild
 
  • #3
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edit...
 
Last edited:
  • #4
SammyS
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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 cant 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
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Wait. I see it now, thank's all.
 
Last edited:

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