-a-vector-function-such-as-rt-xti-ytj-what-role-do-the-unit-vectors-i-and-j-play

Question

When differentiating a vector function such as r→(t)=x(t)i^+y(t)j^\overrightarrow{r}\left(t)\right.=x\left(t\right)\hat{i}+y\left(t\right)\hat{j}, what role do the unit vectors i^\hat{i} and j^\hat{j} play?

Accepted Answer

They are constants, so only the scalar component functions are differentiated

Answer

They are combined into a single magnitude before differentiation

Answer

They are time-dependent, so they must also be differentiated in every problem

Answer

They are removed after the first derivative because velocity is a scalar

When differentiating a vector function such as r→(t)=x(t)i^+y(t)j^\(\overrightarrow{r}\)\(\left\)(t)\(\right\).=x\(\left\)(t\(\right\))\(\hat{i}\)+y\(\left\)(t\(\right\))\(\hat{j}\), what role do the unit vectors i^\(\hat{i}\) and j^\(\hat{j}\) play?

When differentiating a vector function such as $\vec{r} (t) = x (t) \hat{i} + y (t) \hat{j}$ , what role do the unit vectors $\hat{i}$ and $\hat{j}$ play?