Question

What is the difference between vectors and scalars? Provide examples of each.

Answer 1

A scalar quantity is a one dimensional measurement of a quantity, like temperature, or mass.  A vector has more than one number associated with it.   A simple example is velocity.  It has a magnitude, called speed, as well as a direction, like North or Southwest or 10 degrees west of North.  You can have more that two numbers associated with a vector.  For example you can add a height dimension to velocity and say, for example, ' I am going uphill at a 5 degree slope in the Northeast direction'.    Vectors are frequently broken down into their components along an orthogonal coordinate system, like the x and y axes.   So you can say the y-component of my speed is 3 km/sec and the x-component of my speed is 4 km/sec.   The magnitude, or speed is the square root of the sum of the individual components, 5 in this case.  The direction with respect to the x-axis would be given by the arctangent of Vy / Vx or 36.9 degreesj


.Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude. The speed is the magnitude of the velocity. A car has a velocity of 40 mph east. It has a speed of 40 mph.