Background
Let $$\vec{y}= \left[ {\begin{array}{cc} 5 \\ 1 \\ 10 \\ \end{array} } \right]$$
and $$\vec{u}=\left[ {\begin{array}{cc} -7 \\ 3 \\ -3 \\ \end{array} } \right]$$
Calculate the distance $d$ from $\vec{y}$ to the line through $\vec{u}$ and the origin.
My work so far
Using the formula
$$d=\left|\vec{y}-\frac{\vec{y}\cdot\vec{u}}{|\vec{u}|}{\vec{u}}\right|$$
and plugging in
$$d=\left|\begin{pmatrix}5\\1\\10\end{pmatrix}-\frac{-62}{67}\begin{pmatrix}-7\\3\\-3\end{pmatrix}\right|$$
and then calculating
$$\frac{11\sqrt{38}}{\sqrt{67}}=8.284133.$$
Am I on the right track here? Or, where did I go wrong?
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