$A$ displacement vector has a $Y$-axis component of $10$ units. If it makes an angle of $30^{\circ}$ with the $X$-axis,find the magnitude of the vector.

$A$ force of $5 \ N$ acts on a particle along a direction making an angle of $60^{\circ}$ with the vertical. Its vertical component will be $......... \ N$.

$A$ force of $5\, N$ acts on a particle along a direction making an angle of $60^\circ$ with the vertical. Its vertical component is.......$N$.

The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis, the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).

$A$ vector is represented by $3\,\hat i + \hat j + 2\,\hat k$. Its length in the $XY$ plane is

$A$ person pushes a box kept on a horizontal surface with a force of $100\,N$ as shown in the figure. In unit vector notation,the force $\vec{F}$ can be expressed as?