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01Introduction to Vectors

# 01Introduction to Vectors - INTRODUCTION TO VECTORS A...

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I NTRODUCTION TO V ECTORS A scalar is a quantity that has magnitude but no direction. You can have signed scalar quantities as well. A vector is a quantity that has both magnitude and direction . Some examples of scalar quantities are length, temperature (signed), and mass. Some examples of vector quantities are force, acceleration, displacement, and velocity. To specify the velocity of a moving point in the coordinate plane, we must give both the rate at which the point moves (speed) and the direction of that motion. The velocity vector incorporates both pieces of information. The length of the vector represents its magnitude and its direction is represented by the direction of the arrow that represents the vector. A vector u is represented in boldface, but for our purposes, we will use u . There are a number of different ways to express a vector. When we describe vectors, it is usual to do so by expressing them in terms of a basis .

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