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the point A{x1,y1,z1}and B{x2,y2,z2}lie in the plane ax+by+cz=d.Show that a{x2-x1}+b{y2-y1}+c
{z2-z1}=0.Hence prove thatthe vector ABis perpendicular to ai+bj+ck
Hi NIcolaus~
Sorry for the late response...
Substitute the point A into ax+by+cx = d: ax1 + by1 + cz1 = d and the same for point B: ax2 + by2 + cz2 = d and subtract the 1st from the second getting: a(x2-x1) + b(y2-y1) + c(z2-z1) = d-d = 0. So the first part is done. For the 2nd part, show that the dot product of a(x2-x1) + b(y2-y1) + c(z2-z1) and ai+bj + ck is 0.
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Sherry Wallin
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