Velocity and acceleration vector of a charged particle moving in a magnetic field at some instant are `V=3hati+4hatj` and `a=2hati+xhatj.` Select the correct alternative(s).

Options

A. `x=-1.5`
B. `x=3`
C. Magnetic field is along z-direction
D. Kinetic energy of the particle is constant

Answer

(a,b,c)

Explanation

As `vecFbot vecv, so vecF.vecv=0 implies mveca.vecv=0`
`implies m(2hati+xhatj).(3hati+4hatj)=0`
`implies 6+4x=0 implies x=-1.5`
Let the magnetic field is `vecB=ahati+bhatj+chatk`, then from `vecF=qvecv xx vecB`
`implies m(2hati+xhatj)=q(3hati+4hatj)xx(ahati+bhatj+chatk)`
`implies 2mhati-1.5mhatj=q(3bhatk-3chatj-4ahatk+4chati)`
`4c=2m implies c!=0`
`3b-4a=0 implies b=4/3a`