/*! 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 7: Problem 70

How do you determine if two vectors are orthogonal?

Short Answer

Expert verified
Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is not zero, they are not orthogonal.

Step by step solution

01

Understand Vector Orthogonality

Vector orthogonality or perpendicularity in higher dimensions works analogously to how one understands angles in two dimensions. Two vectors are orthogonal if their dot product is equal to zero.
02

Defining Dot Product

The Dot Product (or Scalar Product) of two vectors is a number (scalar) that is obtained by performing a specific operation on the coordinate vectors. For two vectors \( \mathbf{a} = [a_1, a_2] \) and \( \mathbf{b} = [b_1, b_2] \), the dot product is defined as \( \mathbf{a} \cdot \mathbf{b} = a_1 \cdot b_1 + a_2 \cdot b_2 \).
03

Check for Orthogonality

If \( \mathbf{a} \cdot \mathbf{b} = 0 \), then the two vectors are orthogonal. Plug in the vector coordinates into the dot product formula and simplify. If the result is zero, the vectors are orthogonal. If not, they are not 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

Solve: \(2 x^{\frac{2}{3}}-3 x^{\frac{1}{3}}-20=0\)

Explaining the Concepts Describe how to graph a polar equation.

Use a graphing utility to graph the polar equation. $$r=4 \sin 6 \theta$$

Solve and graph the solution set on a number line: $$ |2 x+3| \leq 13 $$

Use a graphing utility to graph the polar equation. $$r=2+4 \cos \theta$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and 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.