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Math Help - Surface Normal

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    Surface Normal

    How do I find the normal vector to the plane (x, y, z) = (1, 2, 3) + t(2, 3, 4) + s(4, 5, 6) , it goes through origo..?
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    Quote Originally Posted by weasley74 View Post
    How do I find the normal vector to the plane (x, y, z) = (1, 2, 3) + t(2, 3, 4) + s(4, 5, 6) , it goes through origo..?
    r(s,t)=(1+2t+4s,2+3t+5s,3+4t+6s)

    the normal vector is given by

     \frac{\partial r}{\partial t} \times \frac{\partial r}{\partial s}

    \begin{vmatrix}<br />
\vec i && \vec j && \vec k \\<br />
2 && 3 && 4 \\<br />
4 && 5&& 6 \\<br />
\end{vmatrix}=(18-20)\vec i - (12-16) \vec j + (10-12) \vec k =-2 \vec i +4 \vec j -2 \vec k<br />
    Last edited by TheEmptySet; April 9th 2008 at 12:59 PM. Reason: errors
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