Calculus grade 12 lines and planes

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Find the value of k so that the line [x,y,z] = [2,-2,0]+ t[2,k,-3] is parallel to the plane kx +2y - 4z= 12

  • Calculus grade 12 lines and planes -

    a normal to kx + 2y - 4z = 12 is (k,2,-4)

    direction of the given line is (2, k, -3)

    if the line is parallel to the plane, it must be perpendicular to the normal
    that is,
    their dot product = 0

    (k,2,-4)o(2,k,-3) = 0
    2k + 2k + 12 = 0
    4k = -12
    k = -3

  • Calculus grade 12 lines and planes -

    Thank you!!

  • Calculus grade 12 lines and planes -

    yes

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