# Perpendicular vector using dot not cross product.

Alex1976

## 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

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## Answers and Replies

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

ehild

Alex1976
edit...

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Staff Emeritus
Homework Helper
Gold Member
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 $$\vec{C}$$ 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 $$\vec{C}\,.$$

Alex1976
Wait. I see it now, thank's all.

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