For the given vector $\vec{A} = 3\hat{i} - 4\hat{j} + 10\hat{k}$,the ratio of the magnitude of its component on the $x-y$ plane to the component on the $z$-axis is:

$A$ 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 $\,m$)

If $\vec{A} = \hat{i} A \cos \theta + \hat{j} A \sin \theta$ is a vector,then another vector $\vec{B}$ which is perpendicular to $\vec{A}$ is given by:

Given vector $\vec{A} = 2\hat{i} + 3\hat{j}$,the angle between $\vec{A}$ and the $y$-axis is:

Two forces act on point $A$ along the sides $AC$ and $AB$ of a right-angled triangle $ABC$ (where $\angle A = 90^{\circ}$). The magnitudes of these forces are inversely proportional to the lengths of the sides $AC$ and $AB$ respectively. If $F_1 = 1/AC$ and $F_2 = 1/AB$,then the resultant of these forces is proportional to:

Find the angle the vector $\sqrt{3} \hat{i} - \hat{j}$ makes with the positive $x$-axis. (in $^{\circ}$)