Calculus grade 12 lines and planes
posted by Baljinder .
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

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 
Thank you!!

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