A vector `vec(a)` is turned without a change in its length through a small angle `d theta`. Find the value of `|Deltavec(a)|` and `Delta a`.

Options

A. 0,`adtheta`
B. `adtheta`,0
C. 0,0
D. none of these

Answer

B

Explanation

From the figure `|vec(OA)|=a` and `|vec(OB)|=a`
Also from triangle rule `vec(OB)-vec(OA)=vec(AB)=triangleveca`
`implies|triangleveca|=AB`
Using angle `=(arc)/("radius")`
`impliesAB=a.dtheta`
`trianglea` means change in magnitude of vector i.e., `|vec(OB)|-|vec(OA)|`
`impliesa-a=0`
So `trianglea=0`