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Math Help - Projection of point onto line

  1. #1
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    Projection of point onto line

    Find the projection of \begin{pmatrix}-2\\2\\7\end{pmatrix} on the direction of the line \mathbf{x}=\begin{pmatrix}1\\0\\2\end{pmatrix}+\la  mbda\begin{pmatrix}-1\\1\\2\end{pmatrix}

    I'm used to finding the projection of a vector onto another vector. But this has confused me a little as it is the projection of the vector onto a line
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Find the projection of \begin{pmatrix}-2\\2\\7\end{pmatrix} on the direction of the line \mathbf{x}=\begin{pmatrix}1\\0\\2\end{pmatrix}+\la  mbda\begin{pmatrix}-1\\1\\2\end{pmatrix}

    I'm used to finding the projection of a vector onto another vector. But this has confused me a little as it is the projection of the vector onto a line
    It's exactly the same thing- the only use you make of the vector is to determine the line. Here the direction of the line is given by the "coefficient" vector \begin{pmatrix}-1 \\ 1 \\ 2\end{pmatrix}.

    Project onto that vector.
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