What are the rectangular components of a vector ?

Figure shows three forces ${\overrightarrow{F}}_1,{\overrightarrow{F}}_2$ and ${\overrightarrow{F}}_3$ acting along the sides of an equilateral triangle. If the total torque acting at point $O$ (centre of the triangle) is zero then the magnitude of ${\overrightarrow{F}}_3$ is

In an octagon $ABCDEFGH$ of equal side, what is the sum of $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}+\overrightarrow{AG}+\overrightarrow{AH},$ if, $\overrightarrow{\mathrm{AO}}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}}$

If y-component of a force acting in x-y plane is $2\sqrt{3} \mathrm{N}$. Then the x- component will be

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. A vertical force $\overrightarrow{P}$ of magnitude $100 \mathrm{N}$ is applied at point $A$ of the frame.

Suppose the force is $\overrightarrow{P}$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ________.

[Given : $\sin \left(35°\right)=0.573,\cos \left(35°\right)=0.819, \sin \left(110°\right)=0.939,\cos \left(110°\right)=-0.342$]

The resultant of these forces $\overrightarrow{OP},\overrightarrow{OQ},\overrightarrow{OR},\overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately ______$\mathrm{N}.$
[Take $\sqrt{3}=1.7,\sqrt{2}=1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $x, y$ axis]