Example 0.1.Vector equation of a line
0 = 1 + t 0; y 0 = 2 + 2t; z = 4t 0; for some number t 0. Substituting the latter equations into the equation of the plane gives 3(1 + t 0) 2( 2 + 2t 0) + 4t 0 = 5 or t 0 = 4: From the parametric equations for the lines, we then obtain x 0 = 3;y 0 = 10 and z 0 = 16. So the point is ( 3; 10; 16). Example 0.11.Distance D from a point to a plane ... ................
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