1. Find the parametric equation of the line in $R^3$, that passes a point P(1,-2,3) and parallel to $\begin{bmatrix} 2 \ -1 \ 1 \end{bmatrix}$.
Write the answer in two forms; (i) $\begin{bmatrix} x(t) \ y(t) \ z(t) \end{bmatrix} = \begin{bmatrix} \ \ \end{bmatrix} + t \begin{bmatrix} \ \ \end{bmatrix}$ (ii) x(t) = ,y(t) =, z(t) =
2. Find the normal equation of the plane in $R^3$ which passes a point P(2,-1, 5) and orthogonal to $\vec{n} = \begin{bmatrix} 1 \ 3 \ -2 \end{bmatrix}$
