Question

How do you find the equation of a plane through the origin and is parallel to another plane with equation 4x-2y+7z+12=0.

Answer 1

I can use point normal formula? since point is origin so ax+by+cz=0

Answer 2

But how do I get the a, b and c here?

Answer 3

That is the normal?

Answer 4

reuired parallel plane is 4x-2y+7z+k=0 since it passes through (0,0,0) we havve k=0
hence the required plane is 4x-2y+7z=0

Answer 5

Why?

Answer 6

I studied that planes are parallel if and only if their normal vectors are prallel . For normal vectors to be parallel they need to be the scalar multiples of each other?

Answer 7

So why 4, -2 and 7? They can be the scalar multiples of each other too?

Answer 8

@Zeerak plane parallel to ax+by+cz+d=0 is given by ax+by+cz+k=0 where k is to be determined by some other given condition and the one ur saying is valid here

Answer 9

I dont understand apologies :S

Answer 10

Can you please say that again?

Answer 11

@Zeerak as u quoted
"I can use point normal formula? since point is origin so ax+by+cz=0 and But how do I get the a, b and c here"
so a,b,c is proportional to 4,-2,7 i.e a/4 =b/-2=c/7 ....(as the planes are parallel)
i hope now u can ...