JEE Mathematics 2023 Question with Solution

Given: A vector makes an angle of $30^\circ$ with the $y$-axis, and its $y$-component is $2\sqrt{3}$.

Find: The magnitude of the $x$-component.

If a vector of magnitude $V$ makes an angle $\theta$ with the $y$-axis, then

Using the given values,

Since

we get

Cancelling $\sqrt{3}$,

Now the magnitude of the $x$-component is

Therefore, the magnitude of the $x$-component is $2$. The correct option is A.

Given: The angle is measured from the $y$-axis.

Find: The $x$-component.

When the angle is measured from the $y$-axis,

So,

Hence,

Therefore, the magnitude of the $x$-component is $2$.