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Let C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk...

Let `C:vecr(t)=x(t)hati+y(t)hatj+z(t)hatk` be a differentiable curve, i.e. `exists lim_(hto0) (vecr(t+h)-vecr(t))/(h) AA t`
`therefore vecr'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk`
`vecr'(t)` is tangent to the curve `C` at the point `P[x(t),y(t),z(t)]` and points in the direction of increasing `t`.
The tangent vector to `vecr(t)=(2t^(2))hati+(1-t)hatj+(3t^(2)+2)hatk` at `(2,0,5)` is:

A

(a) `4hati+hatj-6hatk`

B

(b) `4hati-hatj+6hatk`

C

(c) `2hati-hatj+6hatk`

D

(d) `2hati+hatj-6hatk`

Text Solution

Verified by Experts

The correct Answer is:
B
(2,0,5) corresponding to r(1) and r'9t)=`4thati-thatj+6t hatk`
so, the required tangent vector is `r'(1)=4hati-hatj+6hatk`.
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