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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 (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

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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