# Find a vector equation and parametric equations for the line

Find a vector equation and parametric equations for the line segment that joins P to Q.
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Steven Arredondo
Given points $P\left(1,-1,8\right)$ and $Q\left(8,2,1\right)$ we have to find the vector equation and parametric equation for the line segment that joins P and Q.
Let,
Thus the vector and parametric equation by the formula.
$\gamma \left(t\right)=\left(1-t\right)\stackrel{\to }{p}+t\stackrel{\to }{Q}$
$⇒\gamma \left(t\right)=\left(1-t\right)<1,-1,8>+t<8,2,1>$
$⇒<1+7t,-1+3t,8-7t>$
$\gamma \left(t\right)=$ assume, where t belongs to closed interval [0,1]
Therefore, vector equation:
$\gamma \left(t\right)=<1+7t,-1+3t,8-7t>$
Parametric equation:
$\left(x\left(t\right),y\left(t\right),z\left(t\right)\right)=\left(1+7t,-1+3t,8-7t\right)$
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