Calculus Grade 12
posted by hanaya .
Determine the value of k such that the points (4,2,6), B(0,1,0) and C(1,0,5) and D (1,k,2) lie on the same plane.

(BA)x(CA) = {4,3,6}x{3,2,11} = {21,26,1}
If D is in the plane of ABC, then (DA)x(CA) will also be normal to the plane of ABC. That is,
{3,k+2,8}x{3,2,11} = {21,26,1}
The plane is
21x+26yz = 26
So,
21+26k+2 = 26
26k = 3
k = 3/26
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