# 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 = ⟨4, 7, 0⟩

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 $v=⟨4,7,0⟩$
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Gennenzip
Step 1 Given: The line through (0, 0, 1) in the direction of the vector$v=<4,7,0>$. To find: Parametric and vector equations of the given line. Step 2 Let, $\stackrel{\to }{{r}_{0}}=\left(0,0,1\right),\stackrel{\to }{d}=<4,7,0>$ The vector equation of the line is, $\stackrel{\to }{r}=\stackrel{\to }{{r}_{0}}+t\stackrel{\to }{d}$
$⇒\stackrel{\to }{r}=<0,0,1>+t<4,7,0>$
$=<0,0,1>+<4t,7t,0>$
$=<0+4t,0+7t,1+0>$
$=<4t,7t,1>$ $⇒\stackrel{\to }{r}=<4t,7t,0>$ The parametric equations of a line are, Result :$x=4t,y=7t,z=0$ Vector equation of a line is, $\stackrel{\to }{r}=<4t,7t,0>$ Parametric equations of a line are, $x=4t,y=7t,z=0.$
Jeffrey Jordon