Two forces having magnitude $A$ and $\frac{ A }{2}$ are perpendicular to each other. The magnitude of their resultant is
Two forces having magnitude $A$ and $\frac{ A }{2}$ are perpendicular to each other. The magnitude of their resultant is
- [JEE MAIN 2023]
- A
$\frac{\sqrt{5}\,A }{4}$
- B
$\frac{5\,A }{2}$
- C
$\frac{\sqrt{5}\,A ^2}{2}$
- D
$\frac{\sqrt{5}\,A }{2}$
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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
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 |