Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q9E

Expert-verified

Essential Calculus: Early Transcendentals

Found in: Page 556

Book edition 2nd

Author(s) James Stewart

Pages 830 pages

ISBN 9781133112280

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

To find a dot product between \({\rm{a}}\) and \({\rm{b}}\).

The dot product \(a \cdot b\) is \( - 15\)

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concept of Dot Product

Formula used:

The dot product of two vectors \({\rm{a}}\) and \({\rm{b}}\) in terms of \(\theta \) is \({\rm{a}} \cdot {\rm{b}} = |{\rm{a}}||{\rm{b}}|\cos \theta \).

Step 2: Calculation of the dot product

The given magnitude of two vectors are \(|{\rm{a}}| = 6\) and \(|{\rm{b}}| = 5\) with angle \(\frac{{2\pi }}{3}\) between them.

Substitute \(|{\rm{a}}| = 6,|\;{\rm{b}}| = 5\), and \(\theta = \frac{{2\pi }}{3}\) in above formula and obtain the dot product as follows.

\(\begin{aligned}{l}{\rm{a}} \cdot {\rm{b}} &= (6)(5)\cos \left( {\frac{{2\pi }}{3}} \right)\\{\rm{a}} \cdot {\rm{b}} &= 30( - 0.5)\\{\rm{a}} \cdot {\rm{b}} &= - 15\end{aligned}\)

Thus, the dot product between two vector \({\rm{a}}\) and \({\rm{b}}\) is \(a \cdot b = - 15\).

Most popular questions for Math Textbooks

To find the three angles of the triangle.

Determine the dot product of the vector\(a\)and\(b\)and verify\(a \times b\) is orthogonal on both\(a\)and \(b.\)

To find a dot product between \({\rm{a}}\) and \({\rm{b}}\).

To show

(a) \({\rm{i}} \cdot {\rm{j}} = 0,{\rm{j}} \cdot {\rm{k}} = 0\) and \({\rm{k}} \cdot {\rm{i}} = 0\).

(b) \({\rm{i}} \cdot {\rm{i}} = 1,{\rm{j}} \cdot {\rm{j}} = 1\) and \({\rm{k}} \cdot {\rm{k}} = 1\)

Determine the dot product of the vector\(a\)and\(b\)and verify\(a \times b\) is orthogonal on both\(a\)and \(b.\)

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free