21-24 Dot Products Find the indicated quantity, assuming that 𝐮=2 𝐢+𝐣, 𝐯=𝐢-3 𝐣, and 𝐰=3 𝐢+4 𝐣 𝐮

Name: Problem 22, Chapter 9: Algebra and Trigonometry
Uploaded: 2019-06-21T22:33:35-08:00
Duration: 1 min 16 s
Channel: Jerry Zhang
Description: 21-24 Dot Products Find the indicated quantity, assuming that 𝐮=2 𝐢+𝐣, 𝐯=𝐢-3 𝐣, and 𝐰=3 𝐢+4 𝐣 𝐮 ·(𝐯+𝐰)

step 1 For this problem, we are asked to find the dot product of u and the sum of v plus w. In order to

Question

$21-24$ Dot Products Find the indicated quantity, assuming that $\mathbf{u}=2 \mathbf{i}+\mathbf{j}, \mathbf{v}=\mathbf{i}-3 \mathbf{j},$ and $\mathbf{w}=3 \mathbf{i}+4 \mathbf{j}$ $$\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})$$

   $21-24$ Dot Products Find the indicated quantity, assuming
that $\mathbf{u}=2 \mathbf{i}+\mathbf{j}, \mathbf{v}=\mathbf{i}-3 \mathbf{j},$ and $\mathbf{w}=3 \mathbf{i}+4 \mathbf{j}$
$$\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})$$

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 9, Problem 22

Instant Answer

Solved by Expert Jerry Zhang

06/21/2019

Step 1

The vector $\mathbf{v}$ is given as $\mathbf{i}-3\mathbf{j}$, which can be written as $(1, -3)$. The vector $\mathbf{w}$ is given as $3\mathbf{i}+4\mathbf{j}$, which can be written as $(3, 4)$. Adding these two vectors together, we get $(1+3, -3+4) = (4, 1)$. Show more…

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$21-24$ Dot Products Find the indicated quantity, assuming that $\mathbf{u}=2 \mathbf{i}+\mathbf{j}, \mathbf{v}=\mathbf{i}-3 \mathbf{j},$ and $\mathbf{w}=3 \mathbf{i}+4 \mathbf{j}$ $$\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})$$

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Key Concepts

Vector Addition

Vector addition involves combining two or more vectors by adding their corresponding components. This operation results in a new vector, which represents the net effect of the original vectors when placed together head-to-tail. In coordinate form, if vectors are represented as (a, b) and (c, d), their sum is (a+c, b+d).

Dot Product

The dot product (or scalar product) is an operation that combines two vectors to produce a scalar. It is computed as the sum of the products of the corresponding components of the vectors. In algebraic terms, for vectors (a, b) and (c, d), the dot product is ac + bd. The dot product is essential in determining angles between vectors and projections.

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