Find the following. (a) 𝐮 (b) |𝐯| (c) 𝐮+𝐯 (d) (𝐮)/(𝐮) (e) (𝐯)/(𝐯) (f) (𝐮+𝐯)/(𝐮+𝐯) 𝐮=⟨1, (1)

Name: Problem 41, Chapter 11: Calculus Early Transcendental Functions
Uploaded: 2021-07-22T22:45:10-08:00
Duration: 1 min 6 s
Channel: Carson Merrill
Description: Find the following. (a) 𝐮 (b) |𝐯| (c) 𝐮+𝐯 (d) (𝐮)/(𝐮) (e) (𝐯)/(𝐯) (f) (𝐮+𝐯)/(𝐮+𝐯) 𝐮=⟨1, (1)/(2)⟩, 𝐯=⟨2,3⟩

step 1 For the given problem, we'll solve the following, knowing that U is equal to 1, 1 half, and V is

Question

Find the following. (a) $\|\mathbf{u}\|$ (b) $|\mathbf{v}|$ (c) $\|\mathbf{u}+\mathbf{v}\|$ (d) $\quad\left\|\frac{\mathbf{u}}{\|\mathbf{u}\|}\right\|$ (e) $\quad \frac{\mathbf{v}}{\|\mathbf{v}\|} \|$ (f) $\left\|\frac{\mathbf{u}+\mathbf{v}}{\|\mathbf{u}+\mathbf{v}\|}\right\|$ $$\mathbf{u}=\left\langle 1, \frac{1}{2}\right\rangle, \mathbf{v}=\langle 2,3\rangle$$

   Find the following.
(a) $\|\mathbf{u}\|$
(b) $|\mathbf{v}|$
(c) $\|\mathbf{u}+\mathbf{v}\|$
(d) $\quad\left\|\frac{\mathbf{u}}{\|\mathbf{u}\|}\right\|$
(e) $\quad \frac{\mathbf{v}}{\|\mathbf{v}\|} \|$
(f) $\left\|\frac{\mathbf{u}+\mathbf{v}}{\|\mathbf{u}+\mathbf{v}\|}\right\|$
$$\mathbf{u}=\left\langle 1, \frac{1}{2}\right\rangle, \mathbf{v}=\langle 2,3\rangle$$

Calculus Early Transcendental Functions

Ron Larson, Bruce… 6th Edition

Chapter 11, Problem 41

Instant Answer

Solved by Expert Carson Merrill

07/22/2021

Step 1

The norm of a vector $\mathbf{u}=\langle u_1, u_2\rangle$ is given by $\|\mathbf{u}\|=\sqrt{u_1^2+u_2^2}$. So, for $\mathbf{u}=\langle 1, \frac{1}{2}\rangle$, we have $\|\mathbf{u}\|=\sqrt{1^2+\left(\frac{1}{2}\right)^2}=\frac{\sqrt{5}}{2}$. Show more…

Show all steps

Thanks for your feedback!

Find the following. (a) $\|\mathbf{u}\|$ (b) $|\mathbf{v}|$ (c) $\|\mathbf{u}+\mathbf{v}\|$ (d) $\quad\left\|\frac{\mathbf{u}}{\|\mathbf{u}\|}\right\|$ (e) $\quad \frac{\mathbf{v}}{\|\mathbf{v}\|} \|$ (f) $\left\|\frac{\mathbf{u}+\mathbf{v}}{\|\mathbf{u}+\mathbf{v}\|}\right\|$ $$\mathbf{u}=\left\langle 1, \frac{1}{2}\right\rangle, \mathbf{v}=\langle 2,3\rangle$$

Play audio

Feedback

Carson Merrill and 68 other subject Calculus 3 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vector Norm

The vector norm, often referred to as the magnitude or length of a vector, is a measure of the distance from the origin to the point represented by the vector. In Euclidean space, it is computed as the square root of the sum of the squares of its components.

Vector Addition

Vector addition is the operation of combining two vectors by adding their corresponding components. This process results in a new vector, which represents the cumulative effect of the original vectors.

Unit Vector

A unit vector is a vector with a length (or norm) of one. It is obtained by dividing a nonzero vector by its norm, effectively preserving its direction while standardizing its magnitude to one.

Please give Ace some feedback