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

Explanation

From the (figure) `| vec(OA)|=a` and `| vec(OB)|=a`.
Also from triangle rule,
`vec(OB)-vec(OA)=vec(AB)=Deltavec(a)`
`rArr|Delta vec(a)|=AB`
Using angle `=("Arc")/("Radius")rArrAB=a.d theta`
So `|Delta vec(a)|=a d theta`.
`Deltaa` means change in the magnitude of vector, i.e., `|vec(OB)|-|vec(OA)|`
`rArr a-a=0`
So `Delta a=0`