The dot product of two vectors $$\vec{x} = \left\lbrack \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right\rbrack \ \mbox{ and } \ \vec{y} = \left\lbrack \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right\rbrack$$ in ${\mathbb R}^n$ is defined by $\vec{x} \cdot \vec{y} = x_1 y_1 + x_2 y_2 + \ldots + x_n y_n$. The vectors $\vec{x}$ and $\vec{y}$ are called perpendicular if $\vec{x} \cdot \vec{y} = 0$. Any vector in ${\mathbb R}^3$ perpendicular to $$\left[\begin{array}{c} -6\cr 2\cr -7 \end{array}\right]$$ can be written in the form
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