A uni-modular tangentvector on the curve `x=t^2+2,y=4t-5,z=2t^2-6t=2`isa. `1/3(2 hat i+2 hat j+ hat k)`b.`1/3( hat i- hat j- hat k)`c. `1/6(2 hat i+ hat j+ hat k)`d. `2/3( hat i+ hat j+ hat k)`A. `(1)/(3)(2hati+ 2hatj+hatk)`B. `(1)/(3) (hati-hatj-hatk)`C. `(1)/(6)(2hati + hatj + hatk)`D. `(2)/(3)(hati +hatj +hatk)`

A uni-modular tangentvector on the curve `x=t^2+2,y=4t-5,z=2t^2-6t=2`i

1.	A uni-modular tangentvector on the curve `x=t^2+2,y=4t-5,z=2t^2-6t=2`isa. `1/3(2 hat i+2 hat j+ hat k)`b.`1/3( hat i- hat j- hat k)`c. `1/6(2 hat i+ hat j+ hat k)`d. `2/3( hat i+ hat j+ hat k)`A. `(1)/(3)(2hati+ 2hatj+hatk)`B. `(1)/(3) (hati-hatj-hatk)`C. `(1)/(6)(2hati + hatj + hatk)`D. `(2)/(3)(hati +hatj +hatk)`
Answer» Correct Answer - A The position vector of any point at `t` is `vecr = (2+ t^(2) ) hati + (4t -5) hatj + ( 2t^(2) -6) hatk` `rArr (dvecr)/( dt) = 2t hai + 4hatj + ( 4t -6) hatk` `rArr " "(dvecr)/(dt):\|_(t=2) = 4hati +4hatj+2hatk` and `" "\|(dvecr)/(dt)\| :\|_(t=2) = sqrt(16+16+4)=4` Hence, the required unit tangent vector at `t = 2` is `(1)/(3) ( 2hati + 2hatj +hatk)`.

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