The magnitude of the vector `hati+xhatj+3hatk` is half of the magnitude of vector `hati+xhatj+3hatk` The values of x are

Options

A. `-2//3`
B. `1//3`
C. `2//3`
D. `2`

Answer

A

Explanation

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" "]`