Perpendicular vector using dot not cross product.

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SUMMARY

The discussion revolves around finding a vector C that is perpendicular to two given 3D vectors A = 3i - 2j + 4k and B = -2i + 5j - 2k using the dot product. The key equations established are A dot C = 0 and B dot C = 0, which lead to the conclusion that one component of vector C can be freely chosen, allowing for the determination of the other components. The participants confirm that the dot product of perpendicular vectors equals zero, which is crucial for solving the problem.

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  • Understanding of 3D vector notation and operations
  • Knowledge of the dot product and its properties
  • Familiarity with solving linear equations
  • Basic concepts of vector perpendicularity
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Alex1976
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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

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

ehild
 
edit...
 
Last edited:
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 \vec{C} is perpendicular to \vec{A} and to \vec{B}\,, then so is k\,\vec{C}, where k is a scalar, so in general you will be free to choose one of the components of \vec{C}\,.
 
Wait. I see it now, thank's all.
 
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