Find a vector equation and parametric equations for the line.

John Stewart 2021-12-13 Answered

Find a vector equation and parametric equations for the line. The line through the point (0, 14, -10) and parallel to the line x=1+2t, y=63t, z=3+9t

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Expert Answer

Juan Spiller
Answered 2021-12-14 Author has 38 answers

x=1+2t, y=63t, z=3+9t
The direction vector is obtained from the coefficient of t.
v=<2,3,9>
If the position vector pointing at the point (0,14,10) is
r0=0,14,10>, then the vector equation of the line is
r=r0+tv
=<0,14,10>+t<2,3,9>
We can also write it in more tedious "ijk" form:
r=(0i+14j10k)+t(2i3j+9k)
r=(14j10k)+t(2i3j+9k)
The parametric equations form of a line use
x=x0+at
y=y0+bt
z=z0+ct
where <a,b,cv=<2,3,9> from before, and (x0,y0,z0)=(0,14,10), the point on the line
x=0+2t
y=143t
z=10+9t

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stomachdm
Answered 2021-12-15 Author has 33 answers
The answer is the same as in the book. Thanks!

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