Represent the plane curve by a vector-valued function. y=x+1 r(t)=(t)i+(t+1)j

Baublysiz 2021-11-25 Answered
Represent the plane curve by a vector-valued function.
y=x+1
r(t)=(t)i+(t+1)j

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Expert Answer

Supoilign1964
Answered 2021-11-26 Author has 7548 answers
Step 1
Vector-valued Function represented as
\(\displaystyle\vec{{{r}}}{\left({t}\right)}={X}{\left({t}\right)}\hat{{{i}}}+{Y}{\left({t}\right)}\hat{{{j}}}\)
Step 2
Plane Curve is given as
y=x+1
So, let X(t)=t
then Y(t)=t+1
Therefore, Vector-valued Function is
\(\displaystyle\vec{{{r}}}{\left({t}\right)}={X}{\left({t}\right)}\hat{{{i}}}+{Y}{\left({t}\right)}\hat{{{j}}}\)
\(\displaystyle\vec{{{r}}}{\left({t}\right)}={t}\hat{{{i}}}+{\left({t}+{1}\right)}\hat{{{j}}}\)
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