The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

If the sum of two unit vectors is a unit vector, then magnitude of difference is

Two forces of magnitude $3\;N$ and $4\;N $ respectively are acting on a body. Calculate the resultant force if the angle between them is $0^o$

Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^°$. The magnitude of their resultant is

Statement $I :$Two forces $(\overrightarrow{{P}}+\overrightarrow{{Q}})$ and $(\overrightarrow{{P}}-\overrightarrow{{Q}})$ where $\overrightarrow{{P}} \perp \overrightarrow{{Q}}$, when act at an angle $\theta_{1}$ to each other, the magnitude of their resultant is $\sqrt{3\left({P}^{2}+{Q}^{2}\right)}$, when they act at an angle $\theta_{2}$, the magnitude of their resultant becomes $\sqrt{2\left({P}^{2}+{Q}^{2}\right)}$. This is possible only when $\theta_{1}<\theta_{2}$.

Statement $II :$ In the situation given above. $\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}$ In the light of the above statements, choose the most appropriate answer from the options given below

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, $\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }$