Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is. . . . . . . . .

Which of the following is independent of the choice of co-ordinate system

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$

Mark the correct statement :-

Let $\overrightarrow C = \overrightarrow A  + \overrightarrow B$

$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$

$(B)$ $|\overrightarrow C |$  is always greater than $|\overrightarrow A |$

$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$

$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$

Which of the above is correct

$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.