Two boys searching for buried treasure are standing underneath the same tree. one boy walks 12 m east and then 12 m north. the other boy walks 18 m west and then 11 m north. find the scalar product of their net displacements from the tree.

Let

The origin of coordinates the tree

r1 = vector position of the child 1.

r2 = vector position of the child 2

Child 1:

r1 = (12i + 12j)

Child 2:

r2 = (-18i + 11j)

The scalar product will be given by:

r1. r2 = ((12) * ( - 18)) + ((12) * (11)) = - 84

The scalar product of their net displacements from the tree is - 84m ^ 2