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Math Help - planes in 3-space

  1. #1
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    Question planes in 3-space

    Question
    Find an equation for the plane passing through the point (0,4,1) which is parallel to the vectors <1,2,3> and <0,-1,1>.

    Could you please teach me do this question? Thank you very much.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jenny20 View Post
    Question
    Find an equation for the plane passing through the point (0,4,1) which is parallel to the vectors <1,2,3> and <0,-1,1>.

    Could you please teach me do this question? Thank you very much.
    Take:

    P(lambda,mu)=(0,4,1)+lambda(1,2,3)+mu(0,-1,1)

    Then P(lambda,mu) is a point on a plane which passess through (0,4,1), and
    and the plane is parallel to the plane defined by (0,0,0), (1,2,3), (0,-1,1).

    RonL
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  3. #3
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    Hello, Jenny!

    Find an equation for the plane passing through the point P(0,4,1)
    which is parallel to the vectors u = <1,2,3> and v = <0,-1,1>.

    Since the plane is parallel to u and v,
    . . its normal vector n is perpendicular to both u and v.
    Then n is the cross product of u and v.
    Code:
            | i  j  k |
    n   =   | 1  2  3 |  =  5i - j - k  =  <5,-1,-1>
            | 0 -1  1 |

    You have a point P(0,4,1) and normal vector n = <5,-1,-1>

    You can write the equation: .5(x - 0) - 1(y - 4) - 1(z - 1) .= .0

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  4. #4
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    Thank you very much Soroban. Your explanation is very clear to me.

    Also, Thank you very much CaptainBlack.
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