/*! 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. 61 Prove that vectors \(u\) and \(v... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 61 (page 813)

Prove that vectors \(u\) and \(v\) are orthogonal if and only if \(u 路 v = 0\). (This is Theorem 10.19.)

Short Answer

Expert verified

It is proven that vectors \(u\) and \(v\) are orthogonal if and only if \(u 路 v = 0\).

Step by step solution

01

Step 1. Given Information

We have to prove that vectors \(u\) and \(v\) are orthogonal if and only if \(u 路 v = 0\).

Orthogonal vectors are those vectors that are perpendicular to each other.

02

Step 2. Prove

To prove that vectors \(u\) and \(v\) are orthogonal if and only if \(u 路 v = 0\). We will use the formula for the angle between two vectors \(u\) and \(v\) which is \(u\cdot v=\left\|u \right\|\left\|v \right\|cos\theta\).

Since \(u\neq 0,v\neq 0\). So, \(u\cdot v=0 \) is possible only if \(cos\theta=0\).

Thus, \(u 路 v = 0\) if the vectors are orthogonal.

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 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

u脳wandw脳u

Sketch the parallelogram determined by the two vectors (1,2)and (3,鈭�1). How can you use the cross product to find the area of this parallelogram?

What is Lagrange鈥檚 identity? How is it used to understand the geometry of the cross product?

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(1,4,6),Q(鈭�3,5,0),R(3,2,鈭�1)

Find PQ鈫�.

P=(3,6),Q=(鈭�3,鈭�2)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.