vector addition 27 videos
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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 -
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 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 -
Adding Vectors
Precalculus Vectors and Parametric Equations
How to add vectors geometrically two ways.
Displacement Vector Addition Head to Tail Method Parallelogram Method -
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 -
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 Angle Between Vectors
Precalculus Vectors and Parametric Equations
How to compute the angle between two vectors.
dot product angle between vectors position vectors -
Using the Sine and Cosine Addition Formulas to Prove Identities
Precalculus Advanced Trigonometry
How to use the sine and cosine addition formulas to prove the cofunction identities.
the cosine addition formulas the sine addition formulas -
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 -
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 -
Components of a Force
Precalculus Vectors and Parametric Equations
How to define the components of a vector.
forces components resultant vector addition perpendicular -
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 -
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 -
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 -
The Midpoint and Distance Formulas in 3D
Precalculus Vectors and Parametric Equations
How to derive the formula for the midpoint of a segment in three dimensions.
position vectors the vector from point a to point b the midpoint formula vector addition scalar multiplication -
The Cosine Addition Formulas
Precalculus Advanced Trigonometry
How to derive the cosine of a difference formula.
the unit circle the law of cosines the distance formula cosine of a difference formula -
The Sine Addition Formulas
Precalculus Advanced Trigonometry
How to derive the sine of a sum formula.
cosine of a difference formula the cofunction identities the sine of a sum formula -
The Resultant of Two Forces
Precalculus Vectors and Parametric Equations
How to find the resultant of two forces when they are parallel, opposite, or perpendicular in direction.
Forces Resultant Vector Addition Magnitude Direction The Pythagorean Theorem -
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
