Are you sure about your Dot Product?

I always skim read the dot product module of my calculus course. Never really paying attention to its meaning. Another thing that has become a habit due to my laziness is that I read the solutions to math questions without actually practising them…

Not going to bore you more by actually trying to explain to you the concept of the Dot Product and fail at it. Since, I still might not have understood it.

However, I like tricking people with math puzzles. The following one can come in quite handy. So this is how the problem goes:

Step1: Give your friend the correct formula for the Dot Product:

Step2: Solve a dummy problem for them, showing them that it’s a piece of cake:

Step3: This is where it gets fun. Let them try to solve this new problem:

Step4: Without them asking, give them the value of cos(120°) = -0.5

Step5: Hoping our trick works, they would most likely get the result of the dot product to be -1.

Step6: You show them how both the problems are the same by the actual definition of the Dot Product in which the tail of both the vectors…