Find Parametric Equation of a Line | Solution & Examples | Query Point Official

Find Parametric Equation of a Line | Step-by-Step Solution

Find a parametric equation of the line through `\bar u `  and `\bar v` , where

Answer.

    Given that

    let suppose that

    Now, we find the direction vector 

    Here

        `a = 6, b =  - 7` c = 11

    Now parametric equations are

        `x = x_0 + at`

        `\Rightarrow x =  - 6 + 6t`

        `y = y_0 + bt`

        `\Rightarrow y = 3 - 7t`

        `z = z_0 + ct`

        `\Rightarrow z =  - 4 + 11t`

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Frequently Asked Questions (FAQs)

What is the parametric equation of a line?

The parametric equation of a line represents each coordinate of the line as a function of a parameter, usually denoted by t.

Why do we use parametric equations?

Parametric equations are useful because they describe lines in both two-dimensional and three-dimensional space and work even for vertical lines.

What information is required to find a parametric equation of a line?

To find a parametric equation, we need a point on the line and a direction vector.

Is parametric form important for exams?

Yes, parametric equations of lines are commonly asked in university-level Mathematics, Engineering Mathematics, and Vector Analysis exams.

What parameter is usually used?

The parameter t is commonly used, but any variable can be chosen as a parameter.

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