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The vector hat i+x hat j+3 hat k is rot...

The vector ` hat i+x hat j+3 hat k` is rotated through an angle `theta` and doubled in magnitude, then it becomes `4 hat i+(4x-2)dot hat j+2 hat k` . Then value of `x` are `-2/3` (b) `1/3` (c) `2/3` (d) 2

A

`{-(2)/(3),2}`

B

`((1)/(3),2)`

C

`{(2)/(3),0}`

D

`{2,7}`

Text Solution

Verified by Experts

The correct Answer is:
A
Since, the vector `hati+xhatj+3hatk`k is doubled in magnitude, then it becomes
`4hati+(4x-2)hatj+2hatk`
`therefore 2|hati+xhatj+3hatk|=4hati+(4x-2)hatj+2hatk|`
`implies 2sqrt(2+x^(2)+9)=sqrt(16+(4x-2)^(2)+4)`
`implies 40+4x^(2)=20+(4x-2)^(2)`
`implies 3x^(2)-4x-4=0`
`implies (x-2)(3x+2)=0`
`implies x=2,-(2)/(3)`.
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