Question

Explain why displacement is a vector quantity?

Answer 1

Displacement is defined as the final distance vector minus the initial distance vector.

Let's say you're driving to work in the morning. You first drive north for `5` miles, and then drive east for another `5` miles.

Now let's say that when you get there, you take out a street map. If you were to draw a straight line starting at your house and ending at your workplace, that line would be your displacement vector. That straight line would be `sqrt(50)` miles long, (use the Pythagorean theorem) and it would be pointing northeast. Since the line has a direction, it needs to be a vector quantity. If it weren't a vector quantity, you wouldn't be able to draw it on a map at all, because it would just be a number.

Another reason why displacement needs to be a vector is because it's defined as a subtraction of two vectors, and a vector minus another vector is always a vector.

Very good explanation with good figures can be on this site http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement