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

Options

A. `r`
B. `2r`
C. `r(1+sqrt(2))`
D. `r(sqrt(2))`

Answer

C

Explanation

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