/*! 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 11 How do you compute the magnitude... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 11

How do you compute the magnitude of \(\mathbf{v}=\left\langle v_{1}, v_{2}\right\rangle ?\)

Short Answer

Expert verified
Answer: The magnitude of the vector \(\mathbf{v}\) can be found using the Pythagorean theorem and is given by \(\|\mathbf{v}\| = \sqrt{v_{1}^{2}+v_{2}^{2}}\).

Step by step solution

01

Identify the given components

The components of the vector \(\mathbf{v}\) are given as \(v_{1}\) and \(v_{2}\). These components correspond to the measures of the adjacent sides in a right triangle.
02

Apply the Pythagorean theorem

The Pythagorean theorem states that, for a right-angled triangle with adjacent side lengths \(a\) and \(b\) and hypotenuse length \(c\), \(a^{2}+b^{2}=c^{2}\). In this case, our side lengths are the components \(v_{1}\) and \(v_{2}\), and \(c\) will represent the magnitude of the vector. Rewrite the theorem as: \(v_{1}^{2}+v_{2}^{2}=c^{2}\).
03

Solve for the magnitude c

To obtain the magnitude \(c\), simply take the square root of both sides of the equation: \(c = \sqrt{v_{1}^{2}+v_{2}^{2}}\).
04

Compute the magnitude of \(\mathbf{v}\)

To compute the magnitude of the vector \(\mathbf{v}\), input the values \(v_{1}\) and \(v_{2}\) into the equation and calculate: \(\|\mathbf{v}\| = \sqrt{v_{1}^{2}+v_{2}^{2}}\).

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

Evaluate the following definite integrals. $$\int_{-1}^{1}\left(\mathbf{i}+t \mathbf{j}+3 t^{2} \mathbf{k}\right) d t$$

Compute the following derivatives. $$\frac{d}{d t}\left(\left(t^{3} \mathbf{i}-2 t \mathbf{j}-2 \mathbf{k}\right) \times\left(t \mathbf{i}-t^{2} \mathbf{j}-t^{3} \mathbf{k}\right)\right)$$

Let \(\mathbf{u}(t)=\left\langle 1, t, t^{2}\right\rangle, \mathbf{v}(t)=\left\langle t^{2},-2 t, 1\right\rangle\) and \(g(t)=2 \sqrt{t}\). Compute the derivatives of the following functions. $$g(t) \mathbf{v}(t)$$

Compute \(\mathbf{r}^{\prime \prime}(t)\) and \(\mathbf{r}^{\prime \prime \prime}(t)\) for the following functions. $$\mathbf{r}(t)=\left\langle 3 t^{12}-t^{2}, t^{8}+t^{3}, t^{-4}-2\right\rangle$$

Evaluate the following definite integrals. $$\int_{1}^{4}\left(6 t^{2} \mathbf{i}+8 t^{3} \mathbf{j}+9 t^{2} \mathbf{k}\right) d t$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.