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3-1.Vectors
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Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$
A
$120$
B
$60$
C
$90$
D
$30$
(JEE MAIN-2019)
Solution
$\begin{array}{l}
2\left| {\vec P + \vec Q} \right| = \left| {\vec P + 2\vec Q} \right|\\
\Rightarrow \,13 + 12\,\cos \,\theta = 10 + 6\,\cos \theta \\
\cos = – \frac{1}{2}\\
\theta = {120^ \circ }
\end{array}$
Standard 11
Physics
Similar Questions
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
| Column $-I$ | Column $-II$ |
| $(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $ | $(i)$ Image |
| $(b)$ $\vec a \, – \,\,\vec c \, = \,\,\vec b$ | $(ii)$ Image |
| $(c)$ $\vec b \, – \,\,\vec a \, = \,\,\vec c $ | $(iii)$ Image |
| $(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$ | $(iv)$ Image |
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