First slide

Motion in a plane

Question

Figure shows three vectors $\large \vec a$ , $\large \vec b$ and $\large \vec c$ , where R is the midpoint of PQ. Then which of the following relations is correct?

Difficult

A

$\overrightarrow a + \overrightarrow b = 2\overrightarrow c$
B

$\overrightarrow a + \overrightarrow b = \overrightarrow c$
C

$\overrightarrow a - \overrightarrow b = 2\overrightarrow c$
D

$\overrightarrow a - \overrightarrow b = \overrightarrow c$

Solution

1st method : From fig

$\overline C = \overline a + \overline {PR} ...................(1)$

$\overline C = \overline b + \overline {QR} ...................(2)$

$but\,\overline {PR} = - \overline {QR}$

$\overline a + \overline b = 2\overline c$

by equation (1) + equation (2)
2nd method : From figure

$\overline b + \overline a = \overline {OS} = 2(\overline {OR} )$

$\Rightarrow \overline a + \overline b = 2\overline c$

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