Components of a Vector

What is the vertical component of a $5\mathrm{N}$ force acting on a particle along a direction making an angle of $60°$ with vertical?

Given three vectors $\overrightarrow{a }=6 \hat{i}-3 \hat{j}$, $\overrightarrow{b }=2 \hat{i}-6 \hat{j}$ and $\overrightarrow{c }= -2 \hat{i}+21 \hat{j}$ such that $\overrightarrow{\alpha }=\overrightarrow{a }+\overrightarrow{b }+\overrightarrow{c }$. Then the resolution of the vector $\overrightarrow{\alpha }$ into components with respect to $\overrightarrow{a }$and $\overrightarrow{b }$is given by :

A bird flies at an angle of ${60}^o$ to the horizontal. Its horizontal component of velocity is $10 {\text{m s}}^{-1}.$ Find the vertical component of velocity in ${\text{m s}}^{-1}.$

The magnitude of resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of the sides of an equilateral triangle taken in order is

If projection of any line on coordinate axes$3, 4$ and $5$, then its length is