# Projection of point onto line

• Jun 3rd 2010, 02:24 AM
acevipa
Projection of point onto line
Find the projection of $\displaystyle \begin{pmatrix}-2\\2\\7\end{pmatrix}$ on the direction of the line $\displaystyle \mathbf{x}=\begin{pmatrix}1\\0\\2\end{pmatrix}+\la mbda\begin{pmatrix}-1\\1\\2\end{pmatrix}$

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
• Jun 3rd 2010, 03:24 AM
HallsofIvy
Quote:

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

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 $\displaystyle \begin{pmatrix}-1 \\ 1 \\ 2\end{pmatrix}$.

Project onto that vector.