Q 6. Explain why there are infinitely... [FREE SOLUTION]

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Chapter 10: Q 6. (page 845)

Explain why there are infinitely many different planes containing any given line in ${鈩�}^{3}$ 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 ${鈩�}^{3}$

Calculation

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

The plane in ${鈩�}^{3}$ 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 ${鈩�}^{3}$ 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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91影视

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

Short Answer

Step by step solution

Given information

Calculation

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91影视

Explain why there are infinitely many different planes containing any given line in 鈩�3What 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

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Applied Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

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