Calc_Lecture_01 - 11 Vectors and the Geometry of Space 11.1...

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Vectors and the Geometry of Space 11
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Vectors in the Plane 11.1
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3 Write the component form of a vector. Perform vector operations and interpret the results geometrically. Write a vector as a linear combination of standard unit vectors. Use vectors to solve problems involving force or velocity. Objectives
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4 Component Form of a Vector
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5 Component Form of a Vector Many quantities in geometry and physics, such as area, volume, temperature, mass, and time, can be characterized by a single real number scaled to appropriate units of measure. These are called scalar quantities, and the real number associated with each is called a scalar. Other quantities, such as force, velocity, and acceleration, involve both magnitude and direction and cannot be characterized completely by a single real number.
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6 A directed line segment is used to represent such a quantity, as shown in Figure 11.1. The directed line segment has initial point P and terminal point Q , and its length (or magnitude ) is denoted by Directed line segments that have the same length and direction are equivalent, as shown in Figure 11.2. Figure 11.1 Figure 11.2 Component Form of a Vector
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7 The set of all directed line segments that are equivalent to a given directed line segment is a vector in the plane and is denoted by v = . In typeset material, vectors are usually denoted by
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Calc_Lecture_01 - 11 Vectors and the Geometry of Space 11.1...

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