Question

Find an equation of a plane passing through the point left parenthesis minus 2 comma minus 2 comma 4 right parenthesis and perpendicular to the vector v with rightwards harpoon with barb upwards on top equal less than minus 4 comma 2 comma 4 greater than .

Answer 1

Since you are given the normal vector of the plane as <-4, 2, 4>, you can write the equation of the plane as
.. -4x +2y -4z = -4(-2) +2(-2) -4(4)
.. -4x +2y -4z = 8 -4 -16 = -12
Multiplying by -1/2 will put the equation into standard form.

2x -y +2z = 6