Write the general expression of v and a (velocity & acceleration) in 3

1.	Write the general expression of v and a (velocity & acceleration) in 3 dimension.
Answer» Given that, Velocity = v ACCELERATION = a We know that, Velocity : Velocity of the PARTICLE is rate of change of position of the particle. In mathematically form, $v=\dfrac{dx}{dt}$ Where, v = velocity x = position of particle t = time The velocity in three dimension is $\vect{r}=xi+yj+zk$ $\dfrac{dr}{dt}=\dfrac{dx}{dt}i+\dfrac{dy}{dt}j+\dfrac{dz}{dt}k$ $v=v_{x}i+v_{y}j+v_{z}k$ Acceleration : Acceleration of the particle is rate of change of velocity of the particle. In mathematically form, $a=\dfrac{dv}{dt}$ Where, a = acceleration v =velocity of particle t = time The acceleration in three dimension is $\vect{v}=v_{x}i+v_{y}j+v_{z}k$ $\dfrac{dv}{dt}=\dfrac{dv_{x}}{dt}i+\dfrac{dv_{y}}{dt}j+\dfrac{dv_{z}}{dt}k$ $a=a_{x}i+a_{y}j+a_{z}k$ Hence, This is required solution.