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The vector hat(i)+xhat(j)+3hat(k) is rot...

The vector `hat(i)+xhat(j)+3hat(k)` is rotated through an angle `theta` and doubled in magnitude then it becomes `4hat(i)+(4x-2)hat(j)+2hat(k)`. The value of x is

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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