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

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

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Supoilign1964
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
$$\displaystyle\vec{{{r}}}{\left({t}\right)}={X}{\left({t}\right)}\hat{{{i}}}+{Y}{\left({t}\right)}\hat{{{j}}}$$
$$\displaystyle\vec{{{r}}}{\left({t}\right)}={t}\hat{{{i}}}+{\left({t}+{1}\right)}\hat{{{j}}}$$