Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations P(−3, −6, −1), Q(−1, −9, −8).

emancipezN 2021-02-25 Answered
Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations P(3,6,1),Q(1,9,8).
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un4t5o4v
Answered 2021-02-26 Author has 105 answers
Two vectors P(x1,y1,z1)andQ(x2,y2,z2) Line segment P to Q : 1) Parametric form is x=x1+at
y=y1+bt
z=z1+ct
Where a=x2x1,b=y2y1,c=z2z1 2) vector valued form is r=<x,y,z> Given vectors P(3,6,1)andQ(1,9,8) Line segment P to Q: Firstly evaluate a, b and c PQ=<x2x1,y2y1,z2z1>
=<(1)(3),(9)(6),(8)(1)>
=<1+3,9+6,8+1>
=<2,3,7> 1) Parametric form is x=x1+at
=3+(2)t
=3+2t
y=y1+bt
=6+(3)t
=63t
z=z1+ct
=1+(7)t
=17t 2) Vector valued function: r(t)=<3+2t,63t,17t>
(3+2t)i+(63t)j+(17t)k Hence 1) vector valued function is r(t)=(3+2t)i+(63t)j+(17t)k 2) Parametric form is x=3+2t
y=63t
z=17t
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