Scalar vs. Vector

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A SCALAR QUANTITY has only magnitude (number or amount). Examples of scalar quantities are: time, the mass of an object, the volume of an object, and density.   In Chapter 2, you learned about 2 scalar quantities, distance and speed.

Scalars are represented by lines drawn to scale. The length of the line represents the magnitude. In the map above, each road segment is a certain length.  [Compare to the scale on a map.  For "scalar", think "scale".]

Scalars are added by ordinary algebraic methods [ 2 m + 5 m = 7 m ].  To find the total distance you traveled from start to finish,  add up all of the individual road lengths regardless of the direction of the road.  This is what your car's odometer does.  Your car's speedometer indicates your speed (how fast only, but not your direction).


A VECTOR QUANTITY has both magnitude (number) and direction. Examples of vector quantities that you studied in the last chapter are: displacement (how far and in what direction), velocity (the speed plus the direction), and acceleration (gravity acts at 9.8 m/s2 downward).

A vector quantity is represented by an arrow drawn to scale. The length of the arrow represents the magnitude of the vector quantity. Where the arrow points represents its direction.

Vectors are added by geometric (triangle) methods.  In the map above, the arrow (vector) from Winston-Salem to Greensboro indicates a distance of about 25 miles to the East.  However, the actual distance you would travel would be slightly greater, as there are no "straight line" roads between the two downtown areas.  Also, your trip might have taken you to Greensboro by going through High Point and Jamestown.   The distance you traveled would have been even greater than by traveling I-40, but the displacement remains the same.


Go to [ Components of a Vector ] page.


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