Perpendicular vector using dot not cross product.

AI Thread Summary
To find a vector C that is perpendicular to both vectors A and B, the dot product equations A · C = 0 and B · C = 0 must be satisfied. The equations derived from the dot products are 3Cx - 2Cy + 4Cz = 0 and -2Cx + 5Cy - 2Cz = 0. The discussion highlights the challenge of solving for the unknowns in C, but it is noted that one component can be freely chosen, allowing for a solution. Ultimately, the realization that a scalar multiple of C will also be perpendicular aids in finding a valid vector. This approach clarifies the method for determining a perpendicular vector using the dot product.
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...
 
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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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