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The resultant of the three vectors vec(O...

The resultant of the three vectors `vec(OA), vec(OB)` and `vec(OC)` shown in figure is

A

r

B

2r

C

`r(1+sqrt(s))`

D

`r(sqrt(2)-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(OC)` and `vec(OA)` are cqual in magnitude and inclined to each other at an angle of `90^(@)`. So their resultant is `sqrt(2r)`. It acts mid-way between `vec(OC)` and `vec(OA)`, ie., along OB. Now, both r and `sqrt(2r)` are along the same line and in the same direction .
Resultant = `r +sqrt(2r) = r (1+sqrt(2))`
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