Calculus Grade 12

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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.

  • Calculus Grade 12 -

    (B-A)x(C-A) = {-4,3,-6}x{-3,2,-11} = {-21,-26,1}

    If D is in the plane of ABC, then (D-A)x(C-A) 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+26y-z = 26

    So,

    21+26k+2 = 26
    26k = 3
    k = 3/26

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