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(D) The magnetic force acting on a charged particle is given by $\vec{F} = q(\vec{v} 	imes \vec{B})$.Since the magnetic force is always perpendicular

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$3\hat i - 4\hat k$

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(D) The magnetic force acting on a charged particle is given by $\vec{F} = q(\vec{v} 	imes \vec{B})$.Since the magnetic force is always perpendicular to the velocity vector,it does no work on the particle.Therefore,the kinetic energy and the speed of the particle remain constant.The initial speed is $v = 5\ m/s$,so the magnitude of the velocity at any time must be $5\ m/s$.Additionally,since the magnetic field is along the $z-$ axis,the force $\vec{F} = q(\vec{v} 	imes B\hat k)$ will always lie in the $x-y$ plane.If the particle starts in the $x-y$ plane,its velocity will remain in the $x-y$ plane for all time.Thus,the velocity cannot have a $z-$ component (i.e.,$\hat k$ component).Option $D$ has a $\hat k$ component,which is impossible.

$A$ particle having some charge is projected in the $x-y$ plane with a speed of $5\ m/s$ in a region having a uniform magnetic field along the $z-$ axis. Which of the following cannot be the possible value of velocity at any time?

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