Question

Find the equation of the plane through (9,3,1) parallel to the plane 8x + y + 8z = 0

Answer 1

for a plane wid equation : \(ax + by + cz = d\)
normal vector = \(\langle a, b, c \rangle \)

Answer 2

since the planes are parallel, they will have `same normal vectors` (upto scaling)

Answer 3

so the equation of required plane will be :
\(8x+y+8z = d\)

Answer 4

you can solve the value of \(d\) by plugging in the given point ^

Answer 5

d=83?

Answer 6

so this is the equation 8x+y+8z=83?

Answer 7

\(\large \color{red}{\checkmark}\)

Answer 8

thanks!

Answer 9

yw