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Question: Figure shows three vectors \(\overset{\rightarrow}{a},\overset{\rightarrow}{b}\)and \(\overset{\righ...

Figure shows three vectors a→,b→\overset{\rightarrow}{a},\overset{\rightarrow}{b}and c→\overset{\rightarrow}{c}, where R is the mid point of PQ. Then which of the following relation is correct ?

A

a→+b→=2c→\overset{\rightarrow}{a} + \overset{\rightarrow}{b} = 2\overset{\rightarrow}{c}

B

a→+b→=c→\overset{\rightarrow}{a} + \overset{\rightarrow}{b} = \overset{\rightarrow}{c}

C

a→−b→=2c→\overset{\rightarrow}{a} - \overset{\rightarrow}{b} = 2\overset{\rightarrow}{c}

D

a→−b→=c→\overset{\rightarrow}{a} - \overset{\rightarrow}{b} = \overset{\rightarrow}{c}

Answer

a→+b→=2c→\overset{\rightarrow}{a} + \overset{\rightarrow}{b} = 2\overset{\rightarrow}{c}

Explanation

Solution

a→+PR→=c→\overset{\rightarrow}{a} + \overset{\rightarrow}{PR} = \overset{\rightarrow}{c} ......(1) and b→+QR→=c→\overset{\rightarrow}{b} + \overset{\rightarrow}{QR} = \overset{\rightarrow}{c} ...(2)

adding (1) and (2)

a→+b→+QR→+PR→=2c→\overset{\rightarrow}{a} + \overset{\rightarrow}{b} + \overset{\rightarrow}{QR} + \overset{\rightarrow}{PR} = 2\overset{\rightarrow}{c} but PR→=−QR→\overset{\rightarrow}{PR} = - \overset{\rightarrow}{QR}

\ a→+b→=2c→\overset{\rightarrow}{a} + \overset{\rightarrow}{b} = 2\overset{\rightarrow}{c}