An object moves from position (3,4) to (6,5) in the xy-plane. Find the magnitude and direction of displacement vector of the particle.

Explanation

Positions of the particle are
`r_(1) = x_(1) hati +y_(1) hatj = 3 hati +4hatj` and `r_(2) = x_(2) hati + y_(2) hatj = 6 hati + 5hatj`
`:.` Displacement vector, `Deltar = (x_(2) - x_(1)) hati +(y_(2)-y_(1)) hati`
`= (6-3) hati + (5-4) hatj = 3 hati +hatj`
`:.` Magnitude of displacement vector,
`|Deltar| = sqrt((3)^(2)+(1)^(2)) = sqrt(10)`
Direction of `Deltar` with x axis,
`theta = tan^(-1) ((Deltay)/(Deltax)) = tan^(-1) ((1)/(3)) ~~ 18.43^(@)`