   Chapter 11.5, Problem 76E

Chapter
Section
Textbook Problem

# Intersection of PlanesIn Exercises 65–68, (a) find the angle between the two planes and (b) find a set of parametric equations for the line of intersection of the planes. 6 x − 3 y + z = 5 − x + y + 5 z = 5

(a)

To determine

To calculate: planes 6x3y+z=5, x+y+5z=5 are given. Find the angle between the planes.

Explanation

Given:

The equation of the two planes are:

6x3y+z=5

And,

x+y+5z=5

Formula used:

The angle between the two planes is given by:

cosθ=|n1n2|n1n2

Calculation:

As we know any two distinct planes in three-space are either parallel or intersect in a line.

Now The angle between two intersecting planes can be determined from the angle between their normal vectors.

Now vectors n1 and n2 are normal to two intersecting planes,

Hence the angle θ between the normal vectors is equal to the angle between the two planes.

The equations of the planes are:

6x3y+z=5

And,

x+y+5z=5

The coordinates of the normal vector are the coefficients of x,y,z in the standard equation of plane

(b)

To determine

To calculate: Find the set of parametric equations for the line of intersection of planes

6x3y+z=5 and, x+y+5z=5

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### What is the lowest score in the following distribution?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### 103/2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find the derivatives of the functions in Problems 1-14. 3.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral, if it exists. sintcostdt

Single Variable Calculus: Early Transcendentals 