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Math Help - planes & vector

  1. #1
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    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...!
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  2. #2
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    Quote Originally Posted by pree View Post
    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.
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