Angle between vector vec{Q} and resultant of (2 overrightarrow{mathrm{Q}}+2 overrightarrow{mathrm{P}

Hindi

3-1.Vectors

medium

The angle between vector $\vec{Q}$ and the resultant of $(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})$ and $(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$ is:

$0^{\circ}$

$\tan ^{-1} \frac{(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})}{2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}}}$

$\tan ^{-1}\left(\frac{P}{Q}\right)$

$\tan ^{-1}\left(\frac{2 Q}{P}\right)$

(JEE MAIN-2024)

Solution

$\overrightarrow{\mathrm{R}}=(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})+(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$

$\overrightarrow{\mathrm{R}}=4 \overrightarrow{\mathrm{Q}}$

Angle between $\vec{Q}$ and $\vec{R}$ is zero

Option $(1)$ is correct

Standard 11

Physics

If $\left| {{{\vec v}_1} + {{\vec v}_2}} \right| = \left| {{{\vec v}_1} – {{\vec v}_2}} \right|$ and ${{{\vec v}_1}}$ and ${{{\vec v}_2}}$ are finite, then

easy

For the resultant of the two vectors to be maximum, what must be the angle between them……. $^o$

easy

Magnitudes of two vector $\overrightarrow A $ and $\overrightarrow B $ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in same direction $(\theta = 0^o).$ $(ii)$ in opposite direction $(\theta = 180^o)$, then give the magnitude of resultant vector.

easy

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

hard

(JEE MAIN-2021)

Two vectors $\vec A\,{\rm{ and }}\vec B$ are such that $\vec A + \vec B = \vec A – \vec B$. Then

medium

The angle between vector $\vec{Q}$ and the resultant of $(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})$ and $(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$ is:

Solution

Similar Questions

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Magnitudes of two vector $\overrightarrow A $ and $\overrightarrow B $ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in same direction $(\theta = 0^o).$ $(ii)$ in opposite direction $(\theta = 180^o)$, then give the magnitude of resultant vector.

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