Question

Find an equation of a plane through the point (2, 1, 2) which is parallel to the plane 1x−2y−4z=7 in which the coefficient of x is 1.

Answer 1

you need a `point` and a `normal vector` to write the equation of plane

Answer 2

a normal vector is <1,-2,-4>

Answer 3

you also have a point through which the plane goes
whats stopping you from writing the equation of plane

Answer 4

ah I just don't get how to write it given those 2 things

Answer 5

Say P(x, y, z) is any other point on the plane :

Answer 6

join the given point to P :

Answer 7

would you agree that the both vectors shown are perpendicular ?

Answer 8

yes

Answer 9

that means the dot product must be 0 ?

Answer 10

yes

Answer 11

(x-2, y-1, z-2) . (1, -2, -4) = 0

thats the equation of plane