What is the difference between Scalar and Vector quantities?

Scalar only has magnitude while vector has both magnitude and direction. What does that mean?|||It means the difference between speed and velocity. You can say a car is traveling at a speed of 60 miles per hour. That is a scalar quantity and has only magnitude. You can also say the car has the velocity 60 miles per hour due north. That is a vector quantity. It has magnitude, 60 miles per hour, and a direction, due north.





If you have two cars, both traveling 60 miles per hour, they have the same scalar quantity of speed. But, if one is traveling due north, and the other is traveling due south, they have very different vector quantities since they are traveling in opposite directions. Their speeds, a scalar quantity, may be the same, but their velocities, a vector quantity, are very different.





..|||Use this "image" in your mind.





On a Cartesian space (an x-y plot), a vector quantity would be represented by two values (one for the x and one for the y).





In vector notation, the vector would be represented by (for example), the value V = [3 4]





This is the vector that goes from the origin (0, 0) to the point (x, y) = (3, 4).





You could represent it by giving its length (5) and its direction (53.13 degrees or 0.9273 radians). In fact, there exists a system like that called "polar notation", but that will be later in the course.





If you wanted to make this vector [3 4] twice as long (but keep the same direction) you could simply multiply it by 2:





2V = 2[3 4] = [6 8]





In this example, the [3 4] is a vector quantity while the 2 is a scalar quantity. The 2 simply multiplies the magnitude of whatever you want it to multiply: it carries no direction information on its own.





The vector quantity [3 4] carries a direction information (53.13 deg.).


Note that the direction of [6 8] is also 53.13 degrees. That is because multiplication by a scalar does not affect direction.





Multiplication by another vector would affect direction (you will see that later).|||A magnitude is a simple value like 10. A simple value doesn't give you any direction. A vector can give you both magnitude and direction, for example 40x+30y is an example of a vector. This vector might describe where you would end up if you went 30 miles east and 40 miles north.|||scalar has simply an amount, while a vector quantity has both an amount and a direction in which the action is occurring.