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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) `-2/3` (B) `1/3` (C) `2/3` (D) 2

A

`1`

B

`-2//3`

C

`2`

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Let `vec alpha = hati + x hatj + 3hatk, vecbeta = 4hati + ( 4x-2)hatj +2hatk`
Given, `2|vecalpha| = | vecbeta|`
or `2sqrt(10+x^(2)) = sqrt(20+ 4( 2x-1)^(2))`
or `10+ x^(2)= 5 + ( 4x^(2) - 4x +1)`
or `3x^(2) - 4x -4=0`
or `x=2, -(2)/(3)
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