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
Statement$-I$ is false but Statement$-II$ is true
Both Statement$-I$ and Statement$-II$ are true
Statement$-I$ is true but Statement$-II$ is false
Both Statement$-I$ and Statement$-II$ are false.
The two vectors $\vec A = -2\widehat i + \widehat j + 3\widehat k$ and $\vec B = 7\widehat i + 5\widehat j + 3\widehat k$ are :-
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
Which of the following is independent of the choice of co-ordinate system
When vector $\overrightarrow{ A }=2 \hat{ i }+3 \hat{ j }+2 \hat{ k }$ is subtracted from vector $\vec{B}$, it gives a vector equal to $2 \hat{j}$. Then the magnitude of vector $\vec{B}$ will be:
What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of $7.0\, m$ pointing in the $X- $direction