Consider the line with these parametric equations: x = -9t + 3 y = 6t - 8 z = -5t + 4 a) One...
Question:
Consider the line with these parametric equations:
$$x = -9t + 3 $$
$$y = 6t - 8 $$
$$z = -5t + 4 $$
a) One set of symmetric equations for this line is
$$\frac{x - 3}{-9} = \frac{y - y_{0}}{b} = \frac{z - z_{0}}{c}, $$
find {eq}y_{0}, \, z_{0}, \, b, {/eq} and {eq}c {/eq}.
b) Another set of symmetric equations for this line is
$$\frac{x}{9} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}, $$
find {eq}y_{1}, \, z_{1}, \, b, {/eq} and {eq}c {/eq}.
Parameterize Line:
A line in three dimensions, a vector, can be parameterized by
constructing a vector to a point on that line plus
a direction vector times a parameter.
Answer and Explanation: 1
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Take the original parametric equations and solve for
the parameter in each equation. Set them all equal .
$$t=\dfrac{x-3}{-9} =...
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Parametric Equations in Applied Contexts
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Chapter 24 / Lesson 6
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Parametric equations are those that involve two or more variables, and are expressed by defining each variable in terms of only one other variable, called the parameter. See how these are found and used by solving several examples of parametric equations applied to real-life contexts.
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