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

Let `C:r(t)=x(t)hati+y(t)hatj+z(t)hatk` be a differentiable curve, i.e., `lim_(xto0) (r(t+H)-r(h))/(h)` exist for all t,
`therefore r'(t)=x'(t)hati+y'(t)hatj+z'(t)hatk`
Iff `r'(t)`, is tangent to the curve C at the point `P[x(t),y(t),z(t)] and r'(t)` points in the direction of increasing t.
Q. The tangent vector to `r(t)=2t^(2)hati+(1-t)hatj+(3t^(2)+2)hatk` at (2,0,5) is

A

`4hati+hatj-6hatk`

B

`4hati-hatj+6hatk`

C

`2hati-hatj+6hatk`

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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