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Chapter 10: Q 17. (page 845)

When a line L intersects a plane 蚁 the angle between them is defined to be the complement of the acute angle between the direction vector for the line and the normal vector to the plane. Draw a figure that illustrates this angle,

and explain why the definition given is a reasonable definition.

Short Answer

Expert verified

The angle described is the minimum angle that the line L can form with the line in the plane 蚁 through Q

Step by step solution

01

Given information

A line L intersecting the plane 鈩�

02

Calculation

The purpose is to illustrate why the complement of the acute angle produced between the line's direction vector and the plane's normal vector is a fair definition of the angle generated when a line encounters a plane.

Assume that Qis the point of intersection of the line and the plane.

03

Calculation

If the line Lis orthogonal to the plane 蚁 then the angle between them is 蟺2

Otherwise, the angle described is the minimum angle that the line L can form with the line in the plane 蚁 through Q

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