A  uni-modular tangent vector at t=2 of the curve x=t2+2,y=4t−5,z=2t2−6t  is

The position vector of any point at t is r→=2+t2i^+(4t−5)j^+2t2−6tk^⇒ dr→dt=2ti^+4j^+(4t−6)k^⇒  dr→dtt=2=4i^+4j^+2k^ and  ∣dr→dt∥t=2=16+16+4=4Hence, the required unit tangent vector at t = 2 is   13(2i^+2j^+k^)