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The vector hati+xhatj+3hatk is rotated t...

The vector `hati+xhatj+3hatk` is rotated through an angle `theta` and doubled in magnitude, then it becomes `4hati+(4x-2)hatj+2hatk`. Then values of `x` are

A

1

B

`(-2)/(3)`

C

`2`

D

`(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
let `alpha=hati+xhatj+3hatk`,
`beta=4hati+(4x-2)hatj+2hatk`
Given, `2|alpha|=|beta|`
`implies 2sqrt(10+x^(2))=sqrt(20+4(2x-1)^(2))`
`implies10+x^(2)=5+(4x^(2)-4x+1)`
`implies3x^(2)-4x-4=0`
`impliesx-2,-(2)/(3)`
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