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,a dtheta`
B. `a dtheta,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)-vecOA= vec(AB)=vecDelta a`
`implies |Deltavec a|= AB`
Using angle `= ("area")/("radius")`, we get
AB= a. `d theta`
So `|Delta veca| a= d theta`
`Delta a` means change in magnitude of vector i.e., `|vec(OB)|-|vec(OA)|implies a-a= 0`
So `Delta a= 0`