Question

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.

Answer 1

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