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How to Write the Equation of a Line in Point-Slope Form
Slope of a Line
Finding the Direction of the Line
Explaining the Vector Equation
Vector Equation of a Line in 3 Dimensions
How to Find a Direction Vector
How to find the direction vector given two points on a line
Finding the equation of the line
Finding a scalar product of two vectors
Finding the Position Vector
Vector equation of a line in 2D
Why does the vector equation of a line give us a line?
Using the dot product in 3D
Why does this give a plane?
How many solutions are there to this equation?
Equation of a line through two points
Using vectors to describe an infinite set of points
Finding another point on the line using vectors
Vector equation
Vector equation of a line
Position vector
Position vector in 2 dimensions
Drawing a direction vector
Vector addition
Vector Equation of a Line
What happens when t varies?
What information do we need to find the equation of a line
Example finding the equation of a line given point and direction vector
Parametric equation of the line
Conclusion
3D example
Comparing the Vector Equation to the Cartesian Equation
How to find the position of a particle at any time
Finding a point on a vector equation of a line
Expanding the brackets
Finding the vector equation
What is a gradient?
Multiple Vector Equations for a Single Line
Finding the Vector Parallel to the Line
Conclusion
3D example
Comparing the Vector Equation to the Cartesian Equation
How to find the position of a particle at any time
Finding a point on a vector equation of a line
Expanding the brackets
Finding the vector equation
What is a gradient?
Multiple Vector Equations for a Single Line
Finding the Vector Parallel to the Line
Conclusion