position vector components 27 videos
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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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
Motion Along a Line
Precalculus Vectors and Parametric Equations
How to write equations describing motion in a straight line given the velocity and the position when t=0.
velocity constant velocity position vector equation of a line parametric equations parametric equations of a line -
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 -
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 -
Parametrizing a Line Segment
Precalculus Vectors and Parametric Equations
How to write the parametric equations of a line segment that goes from point A to point B.
vector equation line segment parametric equations -
Evaluating Sine and Cosine at Special Acute Angles
Precalculus Trigonometric Functions
How do we measure sine and cosine of pi/4?
sine cosine unit circle definitions of sine and cosine angles in standard position
