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**Unformatted text preview: **9/23/2008 1 1 Vectors Vectors 2D motion 2D motion 2 " VECTORS have magnitude plus direction " Three ways of representation 1. Graphically as arrow 2. As letter capped by arrow A 3. As boldface letter A 3 VECTORS " Vectors are equal ONLY if they have the same magnitude and direction (and represent the same quantity). " It does not matter that they are drawn at different places. 4 To ADD vectors use tip-to-tail method: A A B A+B B VECTORS 5 A B To SUBTRACT a vector add its negative: A - B = A + (-B) B-B A-B A-B VECTORS 6 Multiplying a vector by a scalar number A 2 A- 0.5 A VECTORS 9/23/2008 2 7 You MUST know this: r = + x 2 + y 2 VECTOR COMPONENTS Magnitude 8 A = A x + A y Components: A x = A cos q A y = A sin q A x and A y are called the vector components of A VECTOR COMPONENTS 9 A = A x + A y Components: A x = A cos q A y = A sin q A x and A y are called the vector components of A VECTOR COMPONENTS A x = A sin q A y = A cos q q But beware... 10 11 Unit vectors are defined as an aid in dealing with vector components VECTOR COMPONENTS Unit vectors and have magnitude = 1, and always point along the x and y directions as shown. Their only purpose is to describe a direction in space. x y 12 For the time being, restrict consideration to two dimensions represented by the x-y plane. VECTOR COMPONENTS If we write In terms of Unit vectors we get the following A r y A x A A y x Æ Æ + = r Where A x is the x component of the vector and A y is the y component. For simplicity lets use the Following Notation. ) , ( y x A A A = r 9/23/2008 3 13 Depending on a vector s direction, the components Ax and Ay can be positive or negative: VECTOR COMPONENTS y x 3 Æ2 ) 3 , 2 ( +- =- y x A Æ3 Æ2 ) 3 , 2 ( + = = r y x 3 Æ2 ) 3 , 2 (- =- y x 3 Æ2 ) 3 , 2 (-- =-- 14 Problem: A + B = ?...

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