   Chapter 16.6, Problem 1E

Chapter
Section
Textbook Problem

Determine whether the points P and Q lie on the given surface.1. r(u, v) = ⟨u + v, u − 2v, 3 + u − v⟩ P(4, −5, 1), Q(0, 4, 6)

To determine

Whether the point P(4,5,1) lies on the surface r(u,v)=u+v,u2v,3+uv or not and whether the point Q(0,4,6) lies on the surface r(u,v)=u+v,u2v,3+uv or not.

Explanation

Given data:

The surface vector is r(u,v)=u+v,u2v,3+uv and the point is P(4,5,1) .

The surface vector is r(u,v)=u+v,u2v,3+uv and the point is Q(0,4,6) .

The point P(4,5,1) lies on the surface r(u,v)=u+v,u2v,3+uv if and only if there are values for u and v such that the corresponding values of u and v must satisfy the vector r(u,v)=u+v,u2v,3+uv .

Equate x-, y-, and z-coordinates of the point to the corresponding points of the vector r(u,v) and obtain the values of u and v as follows.

u+v=4 (1)

u2v=5 (2)

3+uv=1 (3)

Rearrange the equation (1).

u=4v

Substitute 4v for u in equation (2),

(4v)2v=543v=53v=9v=3

Substitute 3 for v in the expression u=4v ,

u=43=1

Substitute 1 for u and 3 for v in equation (3),

3+13=11=1

The values of u and v are satisfied for the vector r(u,v)

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

Convert the expressions in Exercises 8596 radical form. y7/4

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 5-10, solve for y in terms of x. y(3)=4(2)113(x12)

Calculus: An Applied Approach (MindTap Course List)

Evaluate: a. 2332 b. [(13)3]1/3

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

53. If

Mathematical Applications for the Management, Life, and Social Sciences

True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

For y = 3x + tan x, y = _____. a) 3 + sec x b) 3x sec2 x + 3 tan x c) 3 + sec2 x d) x cos x + sin x

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

If n(A)=12, n(B)=12, n(AB)=5, n(AC)=5, n(BC)=4, n(ABC)=2 and n(ABC)=25, find n(C).

Finite Mathematics for the Managerial, Life, and Social Sciences 