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Magnitude & Direction of a VectorThis page: Magnitude of Vector | Direction of Vector|Practice Problems |Vectors & Ordered Pairs Resultant Vector | pictures of Vectors
A Vector is something that has two and only two defining charactersitcs.
The significance of 'direction' can be seen in the difference between
velocity and speeed. In physics, speed is a pure scalar, or something with a magnitude but no direction --such as 5 m/s. 5 meters per second does not tell us which way the object is moving. It gives us no clue about the direction. All that we know from the speed is the magnitude of the movement. On the other hand,
velocity, in Physics, must be expressed as a vector with both a magnitude and a direction. For instance, 5 m/s Eastward is a velocity becuase it tells you the magnitude of the movement, 5 meters per second,
as well as
the direction which is Eastward.
Magnitude: sizeTo illustrate the idea of magnitude, look at the two red circles below. Circle A has
greater magnitude than circle B.
Practice Problems 
Problem 1 )
What is the direction of the vector pictured on the left?
Direction The direction of the vector is North East or diagonally up and right (Short of measuring the angle with a protractor, we cannot be more exact with this picture) 
Problem 2 What is the magnitude and direction of the vector on the left?
The direction of the vector is 55° North of East, and the vector's magnitude is 2.3. Problem 3) Find the magnitude and direction of vector in the diagram on the left. 
The direction of the vector is 47 ° North of West, and the vector's magnitude is 2.3. Problem 4) Find the magnitude and direction of vector in the diagram on the left. 
The direction of the vector is 43° East of South, and the vector's magnitude is 2.3. It is also possible to describe this vector's direction as 47° South of East. Problem 5) What is the difference between a vector that is 55° north of west and a vector that's 35°west of north?
In terms of direction, there is no difference whatsover between 55°north of west, and 35°west of north. This page: Magnitude of Vector | Direction of Vector|Practice Problems |Vectors & Ordered Pairs Resultant Vector | pictures of Vectors Vectors and Ordered Pairs
How to express a vector as an ordered pair:
In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis.
See picture in own window (easier to see whole picture)  Express the vector below as ordered pairs.
Practice Example 1)
Express the vectors coordinates below as ordered pairs in simplest radical form.
Practice Example 2)
Express the vectors coordinates below as ordered pairs in simplest radical form.
Practice Example 3)
 Answer
Practice Example 4)
Express the vector below as ordered pairs.  Answer |
Graphing Calc
