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Ex 1: Find the Parametric Equations of the Line of Intersection of Two Planes Using Vectors
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Determining the Distance Between a Line and a Point
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Determining the Distance Between a Plane and a Point
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Determining the Angle Between Two Planes
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Graphing a Plane in 3D
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The Equation of a Plane in 3D Using Vectors
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Parametric Equations of Lines in 3D
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The Triple Scalar Product: Volume of a Parallelepiped
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An Application of Cross Products: Torque
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Ex: Find the Area of a Triangle Using Vectors - 3D
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Ex 2: Properties of Cross Products - Cross Product of a Sum and Difference
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Ex 1: Properties of Cross Products - Cross Product of a Sum and Difference
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Ex: Find the Cross Product of Two Vectors
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Vector Cross Products
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Ex: Find the Sum of Scalar Multiples of Two Vectors in 3D (Component Form)
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Ex: Find the Magnitude of a Vector in 3D
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Ex: Vector Projection in Three Dimensions
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Ex: Find the Component of a Vector so Two Vectors are Orthogonal (3D)
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Ex: Dot Product of Vectors - 3D
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Parallel Vectors
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Vectors in Space
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The Equation of a Sphere
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Plotting Points in 3D
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Vector Applications: Force and Work
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Ex: Vector Projection in Two Dimensions
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Proof of the Vector Projection Formula
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Vector Projection
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Proof of the formula for the Angle Between Two Vectors
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Determining the Angle Between Two Vectors
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>Applications of Vectors
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Ex: Find the Trace and Determinant of a 3x3 Matrix Using Eigenvalues
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Ex 2: Find the Eigenvalues and Corresponding Unit Eigenvectors of a 3x3 Matrix
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Ex 1: Find the Eigenvalues and Corresponding Eigenvectors of a 3x3 Matrix
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Ex 2: Find the Eigenvalues and Corresponding Unit Eigenvectors of a 2x2 Matrix
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Ex 1: Find the Eigenvalues and Corresponding Eigenvectors of a 2x2 Matrix
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Ex: Find the Eigenvalues of a 4x4 Matrix
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Ex: Find the Eigenvalues of a 3x3 Matrix
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Ex: Find the Eigenvalues of a 2x2 Matrix (Complex)
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Ex: Find the Eigenvalues of a 2x2 Matrix
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Ex: Find a Value to Make 2x2 Matrix Singular (Eigenvalue Warm Up)
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Ex: Direction and Speed of a Plane in the Wind Using Vectors
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Ex: Find the Coordinates of a Rotated Point Using Vectors
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Ex: Find the Net Force of Three Vectors and the Opposite Force
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Ex: Write a Vector as a Combination of Two Vectors
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Ex: Find the Magnitude of The Difference of Two Vectors and The Difference of Two Magnitudes
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Ex: Find the Difference of Scalar Multiples of Vectors in 2D
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Ex 5: Fine a Vector in Component Form Given an Angle and the Magnitude (180)
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Ex 4: Fine a Vector in Component Form Given an Angle and the Magnitude (90)
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Ex 3: Fine a Vector in Component Form Given an Angle and the Magnitude (60)
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Ex 2: Fine a Vector in Component Form Given an Angle and the Magnitude (45)
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Ex 1: Fine a Vector in Component Form Given an Angle and the Magnitude (30)
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Ex: Dot Product of Vectors From a Graph - 2D
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Ex: Dot Product of Vectors - 2D
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Ex: Determine if Vectors are Linearly Independent or Linearly Dependent (Independent)
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Ex: Find the Difference of Scalar Multiples of Vectors in 2D
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Ex: Find the Difference of Two Vector Given in Linear Combination Form
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Ex: Find the Sum of Two Vectors Given in Linear Combination Form
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Ex: Find the Difference of Two Vectors in Component Form
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Find the Component Form of a Vector Given Magnitude and Direction
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Find the Component Form of a Vector from the Graph of a Vector
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Ex: Find the Unit Vector Given the Graph of a Vector in 2D
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Ex: 2D Vector Scalar Multiplication
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Unit Vector
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Vector Operations
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Introduction to Vectors
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Area Using Determinants
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Cramer’s Rule
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Determinants on the Graphing Calculator
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Ex 2: Determinant of 3x3 Matrix - Cofactor Method
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Ex 1: Determinant of 3x3 Matrix - Cofactor Method
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Ex 2: Determinant of 3x3 Matrix - Diagonal Method
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