VECTORS AND PARAMETRIC FUNCTIONS
Part 1
What is a vector?
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A vector is made up of magnitude and direction.
Magnitude being length Directions being the angle Quantities such as : displacement, velocity, acceleration, and force, are made up of magnitude and direction |
How do we find the vector components?
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To find the vector components, we are going to need:
Example:
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Finding the magnitude and direction
Vectors can be written in component form where the first value represents the x-component and the second value represents the y-component.
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Example:
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Part 2- Parametric Functions
What are parametric functions?
What is a parameter? |
In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter. For example, are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.
A curve given by x = x(t), y = y(t) is called a parametrically defined curve and the functions x = x(t) and y = y(t) are called the parametric equations for the curve. |
Finding Parametric Functions
How do we find the parametric functions?
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If y = f(x) is a function of x we can write parametric equations by writing
x = t and y = f(t). Example: The parabola y = x2 can be represented by the parametric equations: x = t and y = t2 |
Eliminating the parameter
How does one eliminate the parameter ? |
Example:
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Challenging Example