/*! 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} Problem 70 How do you determine if two vect... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 70

How do you determine if two vectors are orthogonal?

Short Answer

Expert verified
To determine if two vectors are orthogonal, calculate their dot product. If the result is zero, the vectors are orthogonal, otherwise they are not.

Step by step solution

01

Understand the concept of orthogonal vectors

Orthogonal vectors are vectors that intersect at a right angle (90 degrees). In terms of their components, vectors are orthogonal if their dot product equals zero.
02

Define the vectors

Let us consider two arbitrary vectors, represented as \( \vec{A} = A_1\hat{i} + A_2\hat{j} + A_3\hat{k} \) and \( \vec{B} = B_1\hat{i} + B_2\hat{j} + B_3\hat{k} \)
03

Calculate the dot product of the vectors

Compute the dot product as \( \vec{A}. \vec{B} = A_1*B_1 + A_2*B_2 + A_3*B_3 \).
04

Check the dot product result

If the result of the dot product equals to zero, \( \vec{A} \) and \( \vec{B} \) are orthogonal, otherwise they are not.
05

Decision based on the result

Basing on the result of the dot product, decide whether the vectors are orthogonal or not.

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

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=\mathbf{i}+2 \mathbf{j}, \quad \mathbf{w}=3 \mathbf{i}+6 \mathbf{j}$$

Find the work done in pushing a car along a level road from point \(A\) to point \(B, 80\) feet from \(A,\) while exerting a constant force of 95 pounds. Round to the nearest foot-pound.

Find the work done when a crane lifts a 6000-pound boulder through a vertical distance of 12 feet. Round to the nearest foot-pound.

Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=\mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-2 \mathbf{i}+5 \mathbf{j}$$

Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=3 \mathbf{i}, \quad \mathbf{w}=-4 \mathbf{j}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

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.