In Problems 9-18, (a) find the dot product 𝐯 ·𝐰 ;(b) find the angle between 𝐯 and 𝐯=3 𝐢+4 𝐣, 𝐰

Name: Problem 15, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2021-06-15T10:38:52-08:00
Duration: 6 min 5 s
Channel: Naresh Bagrecha
Description: In Problems 9-18, (a) find the dot product 𝐯 ·𝐰 ;(b) find the angle between 𝐯 and 𝐯=3 𝐢+4 𝐣, 𝐰=-6 𝐢-8 𝐣

step 1 In this question the given data is that is two vector given that is first is vector v that is eq

Question

In Problems 9-18, (a) find the dot product $\mathbf{v} \cdot \mathbf{w} ;(b)$ find the angle between $\mathbf{v}$ and $\mathbf{v}=3 \mathbf{i}+4 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-8 \mathbf{j}$

   In Problems 9-18, (a) find the dot product $\mathbf{v} \cdot \mathbf{w} ;(b)$ find the angle between $\mathbf{v}$ and 
 $\mathbf{v}=3 \mathbf{i}+4 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-8 \mathbf{j}$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 15

Instant Answer

Solved by Expert Naresh Bagrecha

06/15/2021

Step 1

- $\mathbf{v} = 3\mathbf{i} + 4\mathbf{j}$ has components $v_1 = 3$ and $v_2 = 4$. - $\mathbf{w} = -6\mathbf{i} - 8\mathbf{j}$ has components $w_1 = -6$ and $w_2 = -8$. Show more…

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In Problems 9-18, (a) find the dot product $\mathbf{v} \cdot \mathbf{w} ;(b)$ find the angle between $\mathbf{v}$ and $\mathbf{v}=3 \mathbf{i}+4 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-8 \mathbf{j}$

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Key Concepts

Angle Between Vectors

The angle between two vectors can be determined by relating their dot product to their magnitudes using the formula cos(?) = (v · w) / (||v|| ||w||). This concept allows one to quantify the directional relationship between vectors, and it is widely used in applications ranging from computer graphics to engineering to assess alignment and orientation.

Dot Product

The dot product is an algebraic operation that multiplies two vectors and sums the products of their corresponding components, resulting in a scalar. It provides a quantitative measure of how much one vector extends in the direction of another and is fundamental in geometry and physics for determining projections, work done by a force, and more.

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