The equation 2x1 3x2 6x3 = 4 defines a plane in R3. a. Give its normal vector a. b. Find

Chapter 1, Problem 8

(choose chapter or problem)

Get Unlimited Answers! Check out our subscriptions
QUESTION:

The equation \(2 x_{1}-3 x_{2}-6 x_{3}=-4\) defines a plane in \(\mathbb{R}^{3}\).

a. Give its normal vector a.

b. Find the distance from the origin to the plane by using projection.

c. Find the point on the plane closest to the origin by using the parametric equation of the line through \(0\) with direction vector a. Double-check your answer to part b.

d. Find the distance from the point \(\mathbf{w}=(3,-3,-5)\) to the plane by using projection.

e. Find the point on the plane closest to w by using the parametric equation of the line through w with direction vector a. Double-check your answer to part d.

Not The Solution You Need? Search for Your Answer Here:

Questions & Answers


(3 Reviews)

QUESTION:

The equation \(2 x_{1}-3 x_{2}-6 x_{3}=-4\) defines a plane in \(\mathbb{R}^{3}\).

a. Give its normal vector a.

b. Find the distance from the origin to the plane by using projection.

c. Find the point on the plane closest to the origin by using the parametric equation of the line through \(0\) with direction vector a. Double-check your answer to part b.

d. Find the distance from the point \(\mathbf{w}=(3,-3,-5)\) to the plane by using projection.

e. Find the point on the plane closest to w by using the parametric equation of the line through w with direction vector a. Double-check your answer to part d.

ANSWER:

Step 1 of 9

Given plane: \(2{x_1} - 3{x_2} - 6{x_3} =  - 4\) in \(\text{R}^3\).

Add to cart

Reviews

Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Linear Algebra: A Geometric Approach

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!

Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Linear Algebra: A Geometric Approach

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!

Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Linear Algebra: A Geometric Approach

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!


Study Tools You Might Need

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back