Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q.33 (page 849)

Find a unit vector orthogonal to both \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Short Answer

Expert verified

The unit vector is \(\frac{5}{\sqrt{77}}i-\frac{4}{\sqrt{77}}j-\frac{6}{\sqrt{77}}k \).

Step by step solution

01

Given Information

The given vectors are \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

The orthogonal vector is \(\vec{b}=5i-4j-6k\).

The unit vector \(\hat{b}=\frac{\vec{b}}{|b|}\).

02

Find the unit vector

\(\begin{align*}\hat{b}&=\frac{5i-4j-6k}{\sqrt{5^2+(-4)^2+(-6)^2}}\\&=\frac{5}{\sqrt{77}}i-\frac{4}{\sqrt{77}}j-\frac{6}{\sqrt{77}}k\end{align*}\)

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Use the definition of the derivative to find f'for each function fin Exercises 39-54

f(x)=12x+1

If u and v are vectors in ℝ3 such that u·v=0 and u×v=0, what can we conclude about u and v?

Find a vector in the direction opposite to-4,5,-1 and with magnitude 3.

Find the norm of the vector.v=12,13,14

If u, v and w are three vectors in ℝ3, what is wrong with the expression u×v×w?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision 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.

Sign-up for free