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  • 5 years ago

Given that a, b, c are not all zero, find parametric equations for a line in R^3 that passes through the point (x0,y0,z0) and is perpendicular to the line x=x0+at, y=y0+bt, z= z0+ct

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  1. anonymous
    • 5 years ago
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    We have the direction of the line given represented by the vector <a,b,c> We need a vector perpendicular to that, <d,e,f> For two vectors to be perpendicular we want the dot product to be 0 <a,b,c>.<d,e,f>=0 ad+be+cf=0 by observation one choice is d=bc,e=ac,f=-2ba. We can check this abc+bac-2cba=2abc-2abc=0 now we have the proper direction, and we know it passes through the point (x0,y0,z0) so we can parametrize it as following: x=x0+(bc)t y=y0+(ac)t z=z0+(-2ba)t

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