Find a vector equation and parametric equations for the line

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), Q(8,2,1)
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Expert Answer

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, P=<1,1,8>, Q=<8,2,1>
Thus the vector and parametric equation by the formula.
γ(t)=(1t)p+tQ
γ(t)=(1t)<1,1,8>+t<8,2,1>
<1+7t,1+3t,87t>
γ(t)=<x(t),y(t),z(t)> assume, where t belongs to closed interval [0,1]
Therefore, vector equation:
γ(t)=<1+7t,1+3t,87t>
Parametric equation:
(x(t),y(t),z(t))=(1+7t,1+3t,87t)
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