$A$ force of $5 \, N$ acts at an angle of $60^\circ$ with the vertical. Find the vertical component of the force in $N$.

Find the magnitude and direction of the vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$. What are the components of a vector $\vec{A}=2\hat{i}+3\hat{j}$ along the directions of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$?

What is the component of $3\hat{i} + 4\hat{j}$ along $\hat{i} + \hat{j}$?

The angle made by the vector $\vec{A} = \hat{i} + \hat{j}$ with the $x$-axis is ....... $^\circ$.

$A$ certain vector in the $xy$-plane has an $x$-component of $4 \,m$ and a $y$-component of $10 \,m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $\,m$)

What is the maximum number of components a vector can have when resolved in a plane?