If a particle of charge 1μC is projected into a magnetic field `vecB = (2hati + yhatj- zhatk)` T with a velocity `vecV = (4hati+2hatj - 6hatk)ms^(-1)`, then it passes undeviated. If it is now projected with a velocity `vecV = hati + hatj` , then find the force experienced by it?

Explanation

Charged particle moves in a magnetic field undeviated when `hatV` is parallel or anti parallel to `hatB`
`(V_(k))/(B_(x))=(V_(y))/(B_(y))=(V_(z))/(B_(z))=k,4/2=2/y=(-6)/(-z)`
y=1 z=3
`thereforevecB=(2hati+hatj-3hatk)` `vecF=q(vecVxxvecB)`
`vecF=10^(-6)abs({:(hati,hatj,hatk),(1,1,0),(2,1,-3):})`
`vecF=10^(-6)[i(-3)-hatj(-3)+hatk(-1)]`
`vecF=10^(-6)abs((-3hati+3hatj-hatk))N=sqrt(19)muN`