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An insect crawls from A to B where B is ...

An insect crawls from `A` to `B` where B is the centre of the rectangular slant face. Find the (a) initial and final position vector of the insect and (b) displacement vector of the insect.
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Text Solution

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Initial position vector of insect
`vec(OA)=2hat(j)+hat(k)(m)`
`vec(OB)=3/2hat(i)+hat(j)+1/2hat(k)(m)`
Displacement of insect `vec(AB)`= position vector of `vec(B)`-position vector of `vec(A)`.
`vec(AB)=(3/2-0)hat(i)+(1-2)hat(j)+(1/2-1)hat(k)=3/2hat(i)-hat(j)-1/2hat(k)(m)`
Hence, magnitude of displacement
`|vec(AB)|=sqrt((3/2)^(2)+(1)^(2)+(1/2)^(2))=sqrt(9/4+1+1/4)=sqrt(7/2m)`.
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