Lines in three-dimensional space can be described by using parametrization. The parametric equation of a line through
Theory
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This can also expressed as a vector in this way:
Theory
Example 1
Find a parametric equation for the line through the point
You set up the expression on vector form, which gives you
This can be written on coordinate form like this:
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In three dimensions, we need two equations to describe a line. They’re written like this:
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This is another way of writing the two equations
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and
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When you have a parametric equation of a line, you can find these equations by rearranging the coordinate form of the parametric equation to all be expressions for
Example 2
Find the equation for the line with the parametric equation
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You rearrange the three expressions to get
That makes the equations for the line
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If either
Example 3
Find the equation for the line with this parametric equation
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You can’t solve the
Thus, the equations for the line are
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