If a particle of charge `1 muC` is projected into a magnetic fiels `vec(B)=(2hat(i)+yhat(j)-zhat(k))T` with `a` velocity `vec(V)(4hat(i)+2hat(j)-6hat(k))ms^(-1)`, then it passes undeviated. If it is now projected with a velocity `vec(V)=hat(i)+hat(j)`, then find the force experienced by it

Explanation

Charged particle moves in a magnetic field undeviated when `vec(V)` is parallel or anti parallel to `vec(B)`
`(V_(x))/(B_(x))=(V_(y))/(B_(y))=(V_(z))/(B_(z))=k,(4)/(2)=(2)/(y)=(-6)/(-z),y=1,z=3`
`:. vec(B)=(2hat(i)+hat(j)-3hat(k))vec(F)=q(vec(V)xxvec(B))`
`vec(F)=10^(-6)|{:(hat(i),,hat(j),,hat(k)),(1,,1,, 0),(2,,1,,-3):}|`
`vec(F)=10^(-6)[i(-3)-hat(j)(-3)+hat(k)(-1)]`
`|vec(F)|=10^(-6)|(-3hat(i)+3hat(j)-hat(k))|N=sqrt(19)muN`