Help with Equation of planes???

Question

1) Write down an equation of the plane which passes through the point (3, 7, -4) that is perpendicular to the vector [0,5,-1].

Leave your answer in the form Ax plus By plus Cz = D, where A, B, C are integers.

2) Find an equation of the plane which passes through the point (5, -2, -4) that is parallel to the plane -3x - 2y - 7z = 7.

Leave your answer in the form Ax plus By plus Cz = D, where A, B, C are integers.

Answer 1

the vector [0,5,-1] is called the normal vector of the plane.

already, that is the [A, B, C] !

thus we have .. . .

0x + 5y + (-1)z = D

plug in the point

5(7) - (-4) = D = 39

thus

5y - z = 39

that is the equation of the plane.

again.

the parallel planes have the same normal vectors (or multiples of it)

thus

we have

-3x - 2y - 7z = D

to find D, plug again the point. i hope you can be able to finish the second one.