For the three-dimensional vectors 𝐮 and 𝐯, find the sum 𝐮+𝐯, the difference 𝐮-𝐯, and the magnitu

Name: Problem 16, Chapter 11: Calculus
Uploaded: 2021-06-18T17:20:51-08:00
Duration: 1 min 13 s
Channel: Carson Merrill
Description: For the three-dimensional vectors 𝐮 and 𝐯, find the sum 𝐮+𝐯, the difference 𝐮-𝐯, and the magnitudes 𝐮 and 𝐯. 𝐮=⟨0.3,0.3,0.5⟩, 𝐯=⟨2.2,1.3,-0.9⟩

step 1 So for this problem we have our vector three -dimensional vector that's 0 .3, 0 .5. We're going

Question

For the three-dimensional vectors $\mathbf{u}$ and $\mathbf{v}$, find the sum $\mathbf{u}+\mathbf{v},$ the difference $\mathbf{u}-\mathbf{v},$ and the magnitudes $\|\mathbf{u}\|$ and $\|\mathbf{v}\|$. $$\mathbf{u}=\langle 0.3,0.3,0.5\rangle, \mathbf{v}=\langle 2.2,1.3,-0.9\rangle$$

   For the three-dimensional vectors $\mathbf{u}$ and $\mathbf{v}$, find the sum $\mathbf{u}+\mathbf{v},$ the difference $\mathbf{u}-\mathbf{v},$ and the magnitudes $\|\mathbf{u}\|$ and $\|\mathbf{v}\|$.
$$\mathbf{u}=\langle 0.3,0.3,0.5\rangle, \mathbf{v}=\langle 2.2,1.3,-0.9\rangle$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 11, Problem 16

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Solved by Expert Carson Merrill

06/18/2021

Step 1

This is done by adding the corresponding components of the vectors together. So, we have: $$\mathbf{u}+\mathbf{v} =\langle 0.3+2.2,0.3+1.3,0.5-0.9\rangle =\langle 2.5,1.6,-0.4\rangle$$ Show more…

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For the three-dimensional vectors $\mathbf{u}$ and $\mathbf{v}$, find the sum $\mathbf{u}+\mathbf{v},$ the difference $\mathbf{u}-\mathbf{v},$ and the magnitudes $\|\mathbf{u}\|$ and $\|\mathbf{v}\|$. $$\mathbf{u}=\langle 0.3,0.3,0.5\rangle, \mathbf{v}=\langle 2.2,1.3,-0.9\rangle$$

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Key Concepts

Vector Subtraction

Vector subtraction in three dimensions is done by subtracting the corresponding components of the vectors. This process yields a new vector that represents the directed difference between the two original vectors.

Vector Addition

Vector addition in a three-dimensional space involves adding corresponding components of the vectors. This operation is performed component-wise and results in a new vector whose components are the sums of the corresponding components of the original vectors.

Vector Magnitude

The magnitude of a vector is a measure of its length in Euclidean space. In three dimensions, it is calculated by taking the square root of the sum of the squares of its components. This concept is a fundamental aspect of vector calculations and is used to determine the distance or norm of a vector.

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