Surface area is

The angle made by the vector $(\hat{i} + \hat{j})$ with the $x$-axis and $y$-axis is:

Can the resultant of three vectors of unequal magnitudes be a zero vector?

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \dots$

The component of a vector $\vec{A}$ along a direction making an angle $\theta$ with it is given by $A \cos \theta$. What can be said about the magnitude of this component?

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane. Another vector $\overrightarrow{C}$ lies outside this plane. The resultant $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ of these three vectors: