# Find a vector equation and parametric equations for the line.

Find a vector equation and parametric equations for the line. The line through the point (0, 14, -10) and parallel to the line

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Juan Spiller

The direction vector is obtained from the coefficient of t.
$v=<2,-3,9>$
If the position vector pointing at the point $\left(0,14,-10\right)$ is
${r}_{0}=0,14,-10>$, then the vector equation of the line is
$r={r}_{0}+tv$
$=<0,14,-10>+t<2,-3,9>$
We can also write it in more tedious "ijk" form:
$r=\left(0i+14j-10k\right)+t\left(2i-3j+9k\right)$
$r=\left(14j-10k\right)+t\left(2i-3j+9k\right)$
The parametric equations form of a line use
$x={x}_{0}+at$
$y={y}_{0}+bt$
$z={z}_{0}+ct$
where $$ from before, and $\left({x}_{0},{y}_{0},{z}_{0}\right)=\left(0,14,-10\right)$, the point on the line
$x=0+2t$
$y=14-3t$
$z=-10+9t$

stomachdm
The answer is the same as in the book. Thanks!

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