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n = (a,b,c)

v = (x,y,z)

Whatever the dot product of these vectors equal to, lets call d, the vector n is perpendicular to v. Again, I cannot stay calm and ask WHY?

If we call n = (a,b); v= (x,y) ==> ax+by= d and the slope of this line is -a/b whereas the slope of the vector n is b/a. Yes, they are perpendicular since -a/b * b/a = -1 (tanx * tan(90+x) = -1)

I can visualize and experiment it in 2-D but in 3-D I can't.

Also, how do we define a line that passes through the origin and, for instance (1,1,1). I have trouble transforming my logic from x-y plane to space.

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# The dot product

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