$\begingroup$Does anyone know how to convert the equation of the line to the vector and symmetric forms:
$x=-1-2t$
$y=1+3t$
$z=2+t$
$\endgroup$11 Answer
$\begingroup$The vector form is given simply rewriting the three equations in vector form: $$ \begin{bmatrix} x\\y\\z \end{bmatrix}= \begin{bmatrix} -1\\1\\2 \end{bmatrix}+t \begin{bmatrix} -2\\3\\1 \end{bmatrix} $$
for the symmetric form find $t$ from the three equations: $$ t=\frac{x+1}{-2} \qquad t=\frac{y-1}{3} \qquad t=z-2 $$ so you have: $$ \frac{x+1}{-2}=\frac{y-1}{3}=z-2 $$
$\endgroup$
