sagnuhh

2020-12-07

Equations of lines Find both the parametric and the vector equations of the following lines.
The line through (0, 0, 1) in the direction of the vector $v=\u27e84,7,0\u27e9$

Gennenzip

Skilled2020-12-08Added 96 answers

Step 1 Given: The line through (0, 0, 1) in the direction of the vector$v=<4,7,0>$. To find: Vector and parametric equations for the given line. Step 2 Let, $\overrightarrow{{r}_{0}}=(0,0,1),\overrightarrow{d}=<4,7,0>$ The vector equation of the line is, $\overrightarrow{r}=\overrightarrow{{r}_{0}}+t\overrightarrow{d}$

$\Rightarrow \overrightarrow{r}=<0,0,1>+t<4,7,0>$

$=<0,0,1>+<4t,7t,0>$

$=<0+4t,0+7t,1+0>$

$=<4t,7t,1>$ $\Rightarrow \overrightarrow{r}=<4t,7t,0>$ The parametric equations of a line are, Result :$x=4t,y=7t,z=0$ Vector equation of a line is, $\overrightarrow{r}=<4t,7t,0>$ Parametric equations of a line are, $x=4t,y=7t,z=0.$

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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