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Math Help - Vectors: Intersection

  1. #1
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    Vectors: Intersection

    I can't seem to work out the answer. Help would be appreciated.

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    Q:

    Find an equation of the plane, in the form \bold r \bold . \bold n = p, which contains the line l and the point with the position vector \bold a where  l : \bold r = t ( 2 \bold i + 3 \bold j - \bold k), \bold a = \bold i + 4 \bold k.


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    Thanks in advance.

    P.S. The answer is \bold r \bold .  (4 \bold i - 3 \bold j - \bold k) = 0
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  2. #2
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    Quote Originally Posted by Air View Post
    Q:

    Find an equation of the plane, in the form \bold r \bold . \bold n = p, which contains the line l and the point with the position vector \bold a where  l : \bold r = t ( 2 \bold i + 3 \bold j - \bold k), \bold a = \bold i + 4 \bold k.
    The line passes through the origin because there isn't any constant summand. The vector \overrightarrow{OA} = \vec a = (i + 0 +4k) lies in the plane. Therefore the plane passes through the origin and therefore p = 0.

    Calculate the normal vector \vec n :

    \left|\begin{array}{ccc}i&j&k\\1&0&4\\2&3&-1\end{array} \right| = -12i + 9j + 3k = -3(4i - 3j - k)

    Thus the equation of the plan is

    r(4i - 3j - k)=0
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