Chapter 10: Q 6. (page 845)

Explain why there are infinitely many different planes containing any given line in $ℝ^{3}$ What form does the equation of a plane containing the $x -$ axis have?

Short Answer

Expert verified

The form of the plane containing the $x -$ axes is of the type $a x = d$ with $a$ and $d$ being nonzero constants.

Step by step solution

Given information

The planes in $ℝ^{3}$

Calculation

The goal is to explain why there are an endless number of planes in $ℝ^{3}$ that include any line.

The plane in $ℝ^{3}$ is defined by a point $(a, b, c)$ on the plane and two direction vectors parallel to the plane.

The direction vectors come in a variety of shapes and sizes. That's why each given line in $ℝ^{3}$ can be found on an endless number of different planes.

The equation of the plane containing the $x -$ axes have $y$ and $z$ coordinates equal to $0$

Thus, the form of the plane containing the $x -$ axes is of the type $a x = d$ with $a$ and $d$ being nonzero constants.

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Explain why there are infinitely many different planes containing any given line in $ℝ^{3}$ What form does the equation of a plane containing the $x -$ axis have?

Short Answer

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Given information

Calculation

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Explain why there are infinitely many different planes containing any given line in ℝ3What form does the equation of a plane containing the x-axis have?

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Explain why there are infinitely many different planes containing any given line in $ℝ^{3}$ What form does the equation of a plane containing the $x -$ axis have?