For the given vectors u and 𝐯, evaluate the following expressions. a. 3 𝐮+2 𝐯 b. 4 𝐮-𝐯 3 c. |𝐮+3

Name: Problem 41, Chapter 11: Calculus Early Transcendentals
Uploaded: 2021-10-14T15:54:59-08:00
Duration: 2 min 14 s
Channel: Steven Clarke
Description: For the given vectors u and 𝐯, evaluate the following expressions. a. 3 𝐮+2 𝐯 b. 4 𝐮-𝐯 3 c. |𝐮+3 𝐯| 𝐮=⟨-2,1,-2⟩, 𝐯=⟨1,1,1⟩

step 1 Here I'm given two vectors, U and V, and in the first part I want to work out 3U plus 2v. So all

Question

For the given vectors u and $\mathbf{v},$ evaluate the following expressions. a. $3 \mathbf{u}+2 \mathbf{v}$ b. $4 \mathbf{u}-\mathbf{v}$ 3 c. $|\mathbf{u}+3 \mathbf{v}|$ $$\mathbf{u}=\langle-2,1,-2\rangle, \mathbf{v}=\langle 1,1,1\rangle$$

   For the given vectors u and $\mathbf{v},$ evaluate the following expressions.
a. $3 \mathbf{u}+2 \mathbf{v}$
b. $4 \mathbf{u}-\mathbf{v}$ 3
c. $|\mathbf{u}+3 \mathbf{v}|$
$$\mathbf{u}=\langle-2,1,-2\rangle, \mathbf{v}=\langle 1,1,1\rangle$$

Calculus Early Transcendentals

William Briggs, Lyle… 2nd Edition

Chapter 11, Problem 41

Instant Answer

Solved by Expert Steven Clarke

10/14/2021

Step 1

To do this, we multiply each component of $\mathbf{u}$ by 3 and each component of $\mathbf{v}$ by 2. So, $3 \mathbf{u} = \langle-6,3,-6\rangle$ and $2 \mathbf{v} = \langle 2,2,2\rangle$. Show more…

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For the given vectors u and $\mathbf{v},$ evaluate the following expressions. a. $3 \mathbf{u}+2 \mathbf{v}$ b. $4 \mathbf{u}-\mathbf{v}$ 3 c. $|\mathbf{u}+3 \mathbf{v}|$ $$\mathbf{u}=\langle-2,1,-2\rangle, \mathbf{v}=\langle 1,1,1\rangle$$

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Key Concepts

Vector Addition and Subtraction

Vector addition is the process of adding corresponding components of two vectors to form a new vector, while vector subtraction is the addition of one vector and the negative of another. These operations combine or separate vectors component-wise, which is fundamental in vector algebra.

Vector Magnitude

The magnitude of a vector, also known as its norm or length, is calculated by taking the square root of the sum of the squares of its components. This concept measures the distance of the vector from the origin in the given vector space and is essential in quantifying vectors.

Scalar Multiplication

Scalar multiplication involves multiplying each component of a vector by a constant. This operation scales the vector by the given factor without changing its direction, except in the case where the scalar is negative which reverses the direction.

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