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

Answer 1

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

Answer 2

Thank you!!

Answer 3

yes