A unit tangent vector at t=2 on the curve `x=t^(2)+2, y=4t-5` and `z=2t^(2)-6t` is

Options

A. `1/sqrt(3)(veci+vecj+veck)`
B. `1/3(2veci+2vecj+veck)`
C. `1/sqrt(6)(2veci+vecj+veck)`
D. `1/3(veci+vecj+veck)`

Answer

B

Explanation

`vecr = (vect^(2)+2)hati+(4t-5)hatj + (2t^(2)-6t)hatk`
`rArr (dvecr)/(dt) = 2thati + 4hatj+(4t-6)hatk`
`rArr (dvecr)/(dt)_(r=2) = 4hati+4hatj+2hatk`
`rArr` Unit tangent vector at `t=2` is `1/3(2hati+2hatj+hatk)`