Question

The radius vector $\overrightarrow{r}$ can be represented as :

[Assume $\varphi$ to be the angle it subtends with the horizontal]

• A. $rcos\left(\varphi \right)\hat{i}+rsin\left(\varphi \right)\hat{j}$
• B. $rsin\left(\varphi \right)\hat{i}+rcos\left(\varphi \right)\hat{j}$
• C. $rcos\left(\varphi \right)\hat{i}+rcos\left(\varphi \right)\hat{j}$
• D. $rsin\left(\varphi \right)\hat{i}+rsin\left(\varphi \right)\hat{j}$

Answer 1

The correct option is A $rcos\left(\varphi \right)\hat{i}+rsin\left(\varphi \right)\hat{j}$

The magnitude of the projection of the radius vector on $x$-axis will be equal to $rcos\left(\varphi \right)$

The magnitude of the projection of the radius vector on $y$-axis will be equal to $rsin\left(\varphi \right)$

so, the radius vector $\overrightarrow{r}$ can be represented as $rcos\left(\varphi \right)\hat{i}+rsin\left(\varphi \right)\hat{j}$