An ant starts from the origin and crawls 10   cm along the x -axis and then 20   cm along the y -axis. The dot product of the ant's displacement vector with the position vector of a point that makes 45 ° with the x -axis and has a magnitude of 2   cm is

Step-by-step solution

Ant's displacement vector = 10 i ^ + 20 j ^ = a → Position vector of the given point = 2 cos 45 °   i ^ + 2 sin 45 °   j ^ = i ^ + j ^ = b → Therefore, required dot product will be, a → · b → = 10 i ^ + 20 j ^ · i ^ + j ^ = 10 + 20 = 30   cm