/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 18 Let \(v=\langle w,x,y,z\rangle\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 18 (page 801)

Let \(v=\langle w,x,y,z\rangle\).Describe the sets of points in \(R^4\) satisfying \(||v||=4\).

Short Answer

Expert verified

The sets of points in \(R^4\) satisfying the equation \(||v||=4\) lie on the surface \(w^2+x^2+y^2+z^2=4\).

Step by step solution

01

Step 1. Given Information

The vector \(v=\langle w,x,y,z\rangle\).

02

Step 2. Find the set of points

The points which are unit \(4\) distance from the origin in the set \(R^4\) will satisfy the equation

\(||v||=4\).

Therefore, all the position vectors with terminal point is unit \(4\) distance from the origin are part of the set.

Thus, the points will satisfy the following equation:

\(\sqrt{\left(w-0\right)^2+\left(x-0\right)^2 +\left(y-0\right)^2 +\left(z-0\right)^2 }=4\)

\(w^2+x^2+y^2+z^2=4\)

Thus, the sets of points in \(R^4\) satisfying the equation \(||v||=4\) lie on the surface \(w^2+x^2+y^2+z^2=4\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,3,鈭�2),Q(0,0,3),R(鈭�1,3,6)

If u and v are nonzero vectors in 鈩�3, what is the geometric relationship between u,v and u脳v?

In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

u=2,0,-5,v=-3,7,-1

Find a vector in the direction opposite to-1,-4,-6andwith magnitude 7.

Find the mass of a 30-centimeter rod with square cross sections of side length 2 centimeters, given that the density of the rod x centimeters from the left end is 蟻(x) =10路5+0路01527x2 grams per cubic centimeter.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.