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Find the resultant of the three vectors ...

Find the resultant of the three vectors `vec(OA), vec(OB)` and `vec(OC)` shown in figure. Radius of the circle is R.

A

`2 R`

B

`R( 1 + sqrt(2))`

C

`R sqrt(2)`

D

`R(sqrt(2) - 1)`

Text Solution

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The correct Answer is:
B
`X = R + R cos 45^(@) = R( 1 + (1)/(sqrt(2)))`
`Y = R + R sin 45^(@) = R(1 + (1)/(sqrt(2)))`
`S = sqrt(X^(2) + Y^(2))`
`= sqrt(2) R (1 + (1)/(sqrt(2))) = (sqrt(2) + 1) R`
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