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 |
Consider the below given diagram in which vectors $A$ and $B$ are connected by head and tail.
Resultant vector $\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$
$(a)$ from $(iv)$ it is clear that $\mathrm{c}=\mathrm{a}+\mathrm{b}$
$(iv)$ matches with $(a)$
$(b)$ from (iii) $\mathrm{c}+\mathrm{b}=\mathrm{a}$
$ \Rightarrow \mathrm{a}-\mathrm{c}=\mathrm{b}$
$(iii)$ matches with $(b)$
$(c)$ from $(i)$ $\mathrm{b}=\mathrm{a}+\mathrm{c} \Rightarrow \mathrm{b}-\mathrm{a}=\mathrm{c}$
$(ii)$ matches with $(d)$
$(d)$ from (ii) $-\mathrm{c}=\mathrm{a}+\mathrm{b} \Rightarrow \mathrm{a}+\mathrm{b}+\mathrm{c}=0$
$(i)$ matches with $(c)$
The magnitudes of vectors $\vec A,\,\vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$, the angle between $\vec A$ and $\vec B$ is
Six vectors, $\overrightarrow a$ through $\overrightarrow f$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?
On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
Can the resultant of $2$ vectors be zero
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is