1.

The magnitude of the vector `hati+xhatj+3hatk` is half of the magnitude of vector `hati+xhatj+3hatk` The values of x areA. `-2//3`B. `1//3`C. `2//3`D. `2`

Answer» Correct Answer - A
Given, `i+xj+3k=veca" "...(1)`
`and4i+(4x-2)j+2k=vecb" "...(ii)`
From (ii), `|vecb|=sqrt(16+(4x-2)^(2)+4)=sqrt(16x^(2)-16x+24)`
Also, `|vecb|=2|veca|`
Substituting the values, we get
`sqrt(16x^(2)-16x+24)=2sqrt(10+x^(2))`
Solving, `(x-2)(3x+2)=0`
`thereforex=2,-2//3" "]`


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