What is the Normal of a Direction Vector?

AI Thread Summary
To find the normal of a direction vector, such as (1, 2, -2), one must solve the equation x + 2y - 2z = 0. This equation represents a plane that is normal to the given vector. Any vector lying within this plane will also be considered a normal vector to the original direction vector. Understanding this relationship is crucial for applications in geometry and physics. The discussion clarifies the method for determining normal vectors effectively.
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How may I solve for the normal of a direction vector?

If, for example, the direction vector is (1,2,-2), then what is its normal.
 
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Any normal vector (x, y, z) satisfies (x, y, z).(1, 2, -2) = 0, so you just have to solve the linear equation x + 2y - 2z = 0.
 
The plane x+2y- 2z= 0 is normal to that given vector. Any vector in that plane will be normal to the vector.
 
Ok. Got it, thanks.
 
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