Chapter 12 Notes

# Chapter 12 Notes - The angle between v and w is obtuse if...

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12.1: Vectors in the Plane Two-dimensional vector: Length or magnitude of v is a is the x-component, b is the y component Vector is denoted by ……. . is a scalar Unit vector: Components: Vocabulary: (Directional) Vector: a directed line segment Position vector: is based at the origin, O. 12.2: Vectors in Three Dimensions R = ( x , y , z ) Draw In R 2 : In R 3 : Distance Formula in R 3 : Equation of sphere in R 3 : Equation of a cylinder in R 3 : Equations for the line through in the direction Vector parameterization: Parametric equations: Equations for the line through and Vector parameterization: Parametric equations: 12.3: Dot Product and Angle Between Two Vectors The dot product of two vectors, , , is: The angle,, between two vectors is always less than .

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Unformatted text preview: The angle between v and w is obtuse if The coefficient of is called the component of u along v : Where is the angle between u and v . 12.4: The Cross Product The cross product of vectors is the vecor: The cross product is the unique vector with the following three properties: 1. is orthogonal () to v and w . 2. has length ( = angle between v and w ). 3. forms right-handed system. Properties of cross product Area of parallelogram spanned by v and w Volume of parallelepiped, 12.5: Planes in R 3 An equation of the plane through with normal vector can be written in these three ways: Vector form: Scalar forms: Where...
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Chapter 12 Notes - The angle between v and w is obtuse if...

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