ss_8_4

# ss_8_4 - Section 8.4 Vectors In this section we study...

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Section 8.4 Vectors In this section, we study vectors. Vectors are very useful mathematical tools, and they are especially important for the study of physical applications of mathematics. A vector , denoted in these notes in boldface, like v , is a quantity that has both magnitude and direction . Vectors are frequently represented by arrows. When a vector v is represented by an arrow, the length of the arrow indicates the magnitude and the direction of the arrow indicates the direction of the vector. The magnitude of v is denoted by || v || . If v is a vector and || v || =1 ,then v is called a unit vector .A position vector is a vector that has its initial point (tail) at the origin. The zero vector , indicated by 0 , is the vector having magnitude equal to zero. Two vectors are equal if they have equal magnitude and direction. If u and v are equal, we write u=v . We do not distinguish between translates of vectors; hence, two parallel vectors of equal length pointing in the same direction are equal. We give some examples to show the diﬀerence between vectors and scalars (numbers). The number 3 has magnitude but not direction. Hence, the number 3 is a scalar and not a vector. The velocity

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ss_8_4 - Section 8.4 Vectors In this section we study...

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