unit vectors 35 videos
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Unit Vectors
Precalculus Vectors and Parametric Equations
How to express a vector algebraically in terms of the unit vectors i and j.
unit vectors length magnitude the unit vectors i and j vector addition scalar multiplication component form -
The Cross Product of Vectors
Precalculus Systems of Linear Equations and Matrices
How to compute the cross product of two 3D vectors.
unit vectors components cross product determinant -
Vectors and Planes
Precalculus Vectors and Parametric Equations
How to find a vector normal (perpendicular) to a plane given an equation for the plane.
normal vector position vector perpendicular vectors planes the equation of a plane -
The Vector Equation of a Line
Precalculus Vectors and Parametric Equations
How to write the vector equation of a line.
position vector direction vector vector addition scalar multiple vector equation line -
Addition and Scalar Multiplication of Vectors
Precalculus Vectors and Parametric Equations
How to compute the sum of two vectors or the product of a scalar and a vector.
vector components horizontal component vertical component component form vector addition the zero vector scalar multiplication -
The Angle Between Vectors
Precalculus Vectors and Parametric Equations
How to compute the angle between two vectors.
dot product angle between vectors position vectors -
Adding Vectors
Precalculus Vectors and Parametric Equations
How to add vectors geometrically two ways.
Displacement Vector Addition Head to Tail Method Parallelogram Method -
The Dot Product of Vectors
Precalculus Vectors and Parametric Equations
How to compute the dot product of two vectors.
vector components component form dot product scalar product -
Algebraic Representation of Vectors
Precalculus Vectors and Parametric Equations
How to express a position vector algebraically in component form <a,b>, and how to compute its magnitude.
position vector vector components horizontal component vertical component component form magnitude length -
Vector Operations in 3D
Precalculus Vectors and Parametric Equations
How to perform vector operations like addition, scalar multiplication, the dot product, and finding the magnitude, in three dimensions.
vectors components vector addition scalar multiplication the dot product the scalar product magnitude length three dimensions -
The Geometric Representation of Vectors
Precalculus Vectors and Parametric Equations
How to understand what vectors are, and how they can be represented geometrically.
Magnitude Direction Scalar Vector Directed Line Segment Initial Point Terminal Point -
Components of a Force
Precalculus Vectors and Parametric Equations
How to define the components of a vector.
forces components resultant vector addition perpendicular -
Lines in 3D
Precalculus Vectors and Parametric Equations
How to find the vector and parametric equations of a line when given two points on the line.
the vector equation of a line position vectors direction vector parametric equations -
Area With the Cross Product
Precalculus Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
cross product magnitude of vectors dot product angle between vectors area parallelogram -
Trigonometric Identities
Precalculus Trigonometric Functions
How to use the unit circle to derive the tangent identity and the Pythagorean identity.
identities the unit circle trigonometric identities the Pythagorean identity -
Introduction to the 3D Coordinate System
Precalculus Vectors and Parametric Equations
How to define the components and length of a position vector in three dimensions.
axes coordinates position vector components magnitude length distance origin -
Graphing the Reciprocal Trigonometric Functions
Precalculus Trigonometric Functions
How to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions.
identities the unit circle the cofunction identities the "add Π@" identities -
Graph of the Tangent Function
Precalculus Trigonometric Functions
How to graph y = tan(theta) for 0 <= theta < pi/2.
tangent the unit circle asymptotes -
Area With Determinants
Precalculus Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using a determinant.
parallelogram vectors determinant area -
The Definitions of Sine and Cosine
Precalculus Trigonometric Functions
How we define sine and cosine for all angle measures using the unit circle.
sine cosine right triangle definitions of sine and cosine angles in standard position unit circle definitions of sine and cosine
