kzae220o3
2021-11-12
Answered

Find a vector equation and parametric equations for the line segment that joins P to Q.

$P(1,-1,8),\text{}Q(8,2,1)$

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Steven Arredondo

Answered 2021-11-13
Author has **18** answers

Given points $P(1,-1,8)$ and $Q(8,2,1)$ we have to find the vector equation and parametric equation for the line segment that joins P and Q.

Let,$\overrightarrow{P}=<1,-1,8>,\text{}\overrightarrow{Q}=8,2,1$

Thus the vector and parametric equation by the formula.

$\gamma \left(t\right)=(1-t)\overrightarrow{p}+t\overrightarrow{Q}$

$\Rightarrow \gamma \left(t\right)=(1-t)<1,-1,8>+t<8,2,1>$

$\Rightarrow <1+7t,-1+3t,8-7t>$

$\gamma \left(t\right)=<x\left(t\right),y\left(t\right),z\left(t\right)>$ assume, where t belongs to closed interval [0,1]

Therefore, vector equation:

$\gamma \left(t\right)=<1+7t,-1+3t,8-7t>$

Parametric equation:

$(x\left(t\right),y\left(t\right),z\left(t\right))=(1+7t,-1+3t,8-7t)$

Let,

Thus the vector and parametric equation by the formula.

Therefore, vector equation:

Parametric equation:

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