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