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The vectors vecA is given by vecA = that...

The vectors `vecA` is given by `vecA = thati - (sin pi t)hatj + t^(2)hatk` where t is time. Then which of the following is

A

`|vecA|(at t = 1) = sqrt(2)`

B

`(dvecA)/(dt)(at t = 1) = hati+pi hatj+2hatk`

C

`|vecAxx(dvecA)/(dt)|(at t = 1) = sqrt(2pi^(2)+1)`

D

`vecA. (dvecA)/(dt)(at t = 1) = 4`

Text Solution

Verified by Experts

The correct Answer is:
D
The veloctors ……….
`vecA = t hati - sin pi t hatj + t^(2)hatk`
`vecA(t=1) = hati - sin pi t hat j + hatk`
`|vecA| = sqrt(2)`
`(dvecA)/(dt) = hati - pi cos pi t hatj + 2t hatk`
`(dvecA)/(dt) (t = 1) = (hati+pi hatj + 2hatk)`
`vecAxx(dvecA)/(dt) = (hati+hatk)`
`|vecAxx(dvecA)/(dt)|=- sqrt(2pi^(2)+1)`
`vecA.(dvecA)/(dt) = 1+2=3`
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