An insect crawls 10 m towards east, turns to its right, crawls 8 m, and again turns ot its right, Now crawling a distance of 2 m it turns to its right and stop after moving 2 m more. Fing its net displacement.

Explanation

Net displacement is `vec(OD)`
`vec(OD)=vec(OM)+vec(MD)`
`OD=sqrt((OM)^(2)+(MD)^(2))`
`sqrt((OA-BC)^(2)+(AB-CD)^(2))`
`=sqrt(8^(2)+6^(2))`
`OD=10 m`
In `DeltaOMD`
`tan theta (MD)/(OM)=(6)/(8)=(3)/(4)`
Displacement is 10 m at `theta=tan^(-1)((3)/(4))~~ 37^(@)` S of E
Alternate
`vec(r_(1))=ohat(i)+ohat(j) , vec(r_(f))=8hat(i)-6hat(j)`
` vec(d)=vec(r_(f))-vec(r_i)=(8hat(i)-6hat(j))-(ohat(i)+0hat(j))`
`vec(d)=shat(i)-6hat(j)`