# Math Help - planes & vector

1. ## planes & vector

hi i am new here & pardon me if i am wrong..

i just need some help n this some which i hav been trying 2 solve i dont hav anyother book 2 refer..& its too late 2 ask som1 4 der book...

Q. P is the point (1,1,-1). find the equation of the plane passing through P and at right angles to OP.
ans. x+y-z=3

now i dont know who did that came because there aren't any similar solved example & i have tried all the formulas i know....i'll be really thankful if anyone can help me..
& its probably not a lengthy problem since its a 12th grade sum...!

2. Originally Posted by pree
hi i am new here & pardon me if i am wrong..

i just need some help n this some which i hav been trying 2 solve i dont hav anyother book 2 refer..& its too late 2 ask som1 4 der book...

Q. P is the point (1,1,-1). find the equation of the plane passing through P and at right angles to OP.
ans. x+y-z=3

now i dont know who did that came because there aren't any similar solved example & i have tried all the formulas i know....i'll be really thankful if anyone can help me..
& its probably not a lengthy problem since its a 12th grade sum...!
1. Let R(x,y,z) denote a point which is placed in the plane.

2. Then $\overrightarrow{PR} = (x,y,z)-(1,1,-1)$ is a vector which lies completely in the plane.

3. The vector $\overrightarrow{OP} = (1,1,-1)$ must be perpendicular to the plane, that means it must be perpendicular to $\overrightarrow{PR}$ too:

$(1,1,-1) \cdot ((x,y,z)-(1,1,-1)) = 0$

Expand the brackets.