Q 15. Given the equations x=at+x0,y=bt... [FREE SOLUTION]

Chapter 10: Q 15. (page 845)

Given the equations $x = a t + x_{0}, y = b t + y_{0}, z = c t + z_{0}$ for a line $L$ and $伪 x + 尾 y + 纬 z = 未$ for a plane $蚁$ explain how to determine whether $L$ is orthogonal to $蚁$

Short Answer

Expert verified

The line and the plane are orthogonal if and only if $d = 鉄� a, b, c 鉄�$ and $N = 鉄� 伪, 尾, 纬鉄�$ are scalar multiple of each other.

Step by step solution

Given information

The equations $x = a t + x_{0}, y = b t + y_{0}, z = c t + z_{0}$ for a line $L$ and $伪 x + 尾 y + 纬 z = 未$ for a plane $鈩�$

Calculation

The goal is to show how to figure out whether a line $L$ is orthogonal to a plane $蚁$ Find the direction vector and the normal vectors for the given line and plane.

Calculation

The direction vector for the line $x = a t + x_{0}, y = b t + y_{0}, z = c t + z_{0}$ is $d = 鉄� a, b, c 鉄�$

The normal vector of the plane $伪 x + 尾 y + 纬 z = 未$ is $N = 鉄� 伪, 尾, 纬鉄�$

The line and the plane are orthogonal if and only if $d = 鉄� a, b, c 鉄�$ and $N = 鉄� 伪, 尾, 纬鉄�$ are scalar multiple of each other.

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91影视

Given the equations $x = a t + x_{0}, y = b t + y_{0}, z = c t + z_{0}$ for a line $L$ and $伪 x + 尾 y + 纬 z = 未$ for a plane $蚁$ explain how to determine whether $L$ is orthogonal to $蚁$

Short Answer

Step by step solution

Given information

Calculation

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91影视

Given the equations x=at+x0,y=bt+y0,z=ct+z0for a line Land 伪x+尾y+纬z=未for a plane 蚁explain how to determine whether Lis orthogonal to 蚁

Short Answer

Step by step solution

Given information

Calculation

Calculation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Statistics

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Given the equations $x = a t + x_{0}, y = b t + y_{0}, z = c t + z_{0}$ for a line $L$ and $伪 x + 尾 y + 纬 z = 未$ for a plane $蚁$ explain how to determine whether $L$ is orthogonal to $蚁$