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Two equal vector have a resultant equal ...

Two equal vector have a resultant equal to either of them, then the angle between them will be:

A

`90^(@)`

B

`60^(@)`

C

`120^(@)`

D

`0^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c ) Let two vectors are A andB inclined at an angle `theta`

Resultant of the two vectors A and B
`|R|=sqrt(|A|^(2)+|B|^(2)+2|A||B|costheta)`
observing `theta=o^(@)`gives
`|R|=|A|+|B|, "which is true"`
` Let , |A|=|B|=a`
Accordign to the question , |R|=a
FromEq (i)
`a=sqrt(a^(2)+a^(2)+2aacostheta)`
`impliesa^(2)=a^(2)+a^(2)+2a^(2)cos theta`
`implies2a^(2)cos theta=-a^(2)`
`implies cos theta=-1//2`
`implies theta=120^(@)`

Geometrically , angleSOP`=120^(@)`
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