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.

Question

ganeshie8 · Answer

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

anonymous · Answer

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

ganeshie8 · Answer

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

anonymous · Answer

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

ganeshie8 · Answer

|dw:1421731911992:dw|

ganeshie8 · Answer

Say P(x, y, z) is any other point on the plane : 

|dw:1421731967811:dw|

ganeshie8 · Answer

join the given point to P :  

|dw:1421732006396:dw|

ganeshie8 · Answer

would you agree that  the both vectors shown are perpendicular ?

anonymous · Answer

yes

ganeshie8 · Answer

that means the dot product must be 0 ?

anonymous · Answer

yes

ganeshie8 · Answer

(x-2, y-1, z-2) .  (1, -2, -4) = 0

thats the equation of plane