Distinguish between scalars and vectors with an example each
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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 degrees.