Wribreeminsl

2021-02-02

Find the sets of symmetric and parametric equations of the line that runs parallel to the given vector or line and passes through the given point. (For each line, write the direction numbers as integers.) Point $(-1,\text{}0,\text{}8)$ Parallel to $v=3i\text{}+\text{}4j\text{}-\text{}8k$ The given point is $(-1,\text{}0,\text{}8)\text{}\text{and the vector or line is}\text{}v=3i\text{}+\text{}4j\text{}-\text{}8k.$ (a) parametric equations (b) symmetric equations

jlo2niT

Skilled2021-02-03Added 96 answers

(a)
The parametric equations for a line passing through $({x}_{0},\text{}{y}_{0},\text{}{z}_{0})$ and parallel to the vector
$v=ai\text{}+\text{}bj\text{}+\text{}ck$ are
$x={x}_{0}\text{}+\text{}at,\text{}y={y}_{0}\text{}+\text{}bt,\text{}z={z}_{0}\text{}+\text{}ct$
The required parametric equations are
$x=\text{}-1\text{}+\text{}3t,\text{}y=4t,\text{}z=8\text{}-\text{}8t$
(b)
The parametric equations are
$x=\text{}-1\text{}+\text{}3t,\text{}y=4t,\text{}z=8\text{}-\text{}8t$
Solving for t we have,
$\Rightarrow \text{}t=\text{}\frac{x\text{}+\text{}1}{3},\text{}t=\text{}\frac{y}{4},\text{}t=\text{}\frac{z\text{}-\text{}8}{-8}$

$\Rightarrow \text{}\frac{x\text{}+\text{}1}{3}=\text{}\frac{y}{4}=\text{}\frac{z\text{}-\text{}8}{-8}$

$\Rightarrow \text{}\frac{x\text{}+\text{}1}{3}=\text{}\frac{y}{4}=\text{}\frac{8\text{}-\text{}z}{8}$
Symmetric equations
$\frac{x\text{}+\text{}1}{3}=\frac{y}{4}=\frac{8\text{}-\text{}z}{8}$

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