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

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

A

` -2//3,2`

B

1/3,2

C

2/3,-2

D

2,-1/3

Text Solution

Verified by Experts

The correct Answer is:
A
we have ,
` 2 | hati + xhatj + 3hatk| = | 4hati + ( 4hatx -2) hatj + 2hatk|`
` Rightarrow 2sqrt(x^(2) + 10) = sqrt( 20 + ( 4x -2)^(2)) `
` Rightarrow 4( x^(2) +10) = 20 + ( 4x -2) ^(2)`
` Rightarrow 3x^(2) -4x -4=0 Rightarrow x =2, -2//3`
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