The sum of three vectors is zero as shown in the figure. What will be the magnitudes of vectors $\vec{OB}$ and $\vec{OC}$?

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

Vector $P = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}$ makes an angle with the $z$-axis equal to:

$A$ 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 $\,m$)

Consider a frame made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{P}$ of magnitude $100 \; N$ is applied at point $A$ of the frame. Suppose the force $\overrightarrow{P}$ is resolved into components parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $x \; N$. The value of $x$,to the nearest integer,is ............

The magnitude of vectors $\overrightarrow{ OA }, \overrightarrow{ OB }$ and $\overrightarrow{ OC }$ in the given figure are equal. The direction of $\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }$ with the $x$-axis will be