Q. 21 In Problems 19鈥�22, v1=4,6,聽v2... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 21 (page 632)

In Problems 19鈥�22, $v_{1} = <4, 6>, v_{2} = <- 3, - 6>, v_{3} = <- 8, 4>, v_{4} = <10, 15>$
Which two vectors are orthogonal?

Short Answer

Expert verified

$v_{2}$ and $v_{3}$ are orthogonal.

Step by step solution

Step 1. Given information

The given vectors are

$v_{1} = <4, 6>, v_{2} = <- 3, - 6>, v_{3} = <- 8, 4>, v_{4} = <10, 15>$

Step 2. Find the vectors which are orthogonal.

For finding vectors which are parallel, the angle between vectors should be $90 掳$

We will find the angles between vectors.

For finding the angles between any two vectors $\overset{鈫�}{a}$ and $\overset{鈫�}{b}$ ,

$\cos 胃 = \frac{\overset{鈫�}{a} 路 \overset{鈫�}{b}}{||\overset{鈫�}{a}|| ||\overset{鈫�}{b}||}$

Step 3. Find the angle between v1 and v2.

$\cos 胃 = \frac{v_{1} 路 v_{2}}{||v_{1}|| ||v_{2}||} = \frac{- 12 + (- 36)}{(\sqrt{4^{2} + 6^{2}}) (\sqrt{{(- 3)}^{2} + {(- 6)}^{2}})} = \frac{- 48}{\sqrt{52} 脳 \sqrt{45}}$

These are not orthogonal.

Step 4. Find the angle between v2 and v3.

$\cos 胃 = \frac{v_{2} 路 v_{3}}{||v_{2}|| ||v_{3}||} = \frac{24 + (- 24)}{(\sqrt{{(- 8)}^{2} + 4^{2}}) (\sqrt{{(- 3)}^{2} + {(- 6)}^{2}})} = 0 胃 = 90 掳$

These are orthogonal.

Step 5. Find the angle between v3 and v4.

$\cos 胃 = \frac{v_{3} 路 v_{4}}{||v_{3}|| ||v_{4}||} = \frac{- 80 + 60}{(\sqrt{{(- 8)}^{2} + 4^{2}}) (\sqrt{10^{2} + 15^{2}})} = \frac{- 20}{\sqrt{80} 脳 \sqrt{325}}$

These are not orthogonal.

Step 6. Find the angle between v1 and v4.

$\cos 胃 = \frac{v_{1} 路 v_{4}}{||v_{1}|| ||v_{4}||} = \frac{40 + 90}{(\sqrt{4^{2} + 6^{2}}) (\sqrt{10^{2} + 15^{2}})} = \frac{130}{\sqrt{52} 脳 \sqrt{325}} = 1 胃 = 0 掳$

These are not orthogonal.

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91影视

In Problems 19鈥�22, $v_{1} = <4, 6>, v_{2} = <- 3, - 6>, v_{3} = <- 8, 4>, v_{4} = <10, 15>$
Which two vectors are orthogonal?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the vectors which are orthogonal.

Step 3. Find the angle between v1 and v2.

Step 4. Find the angle between v2 and v3.

Step 5. Find the angle between v3 and v4.

Step 6. Find the angle between v1 and v4.

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91影视

In Problems 19鈥�22, v1=4,6,v2=-3,-6,v3=-8,4,v4=10,15Which two vectors are orthogonal?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the vectors which are orthogonal.

Step 3. Find the angle between v1 and v2.

Step 4. Find the angle between v2 and v3.

Step 5. Find the angle between v3 and v4.

Step 6. Find the angle between v1 and v4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Pure Maths

Logic and Functions

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 19鈥�22, $v_{1} = <4, 6>, v_{2} = <- 3, - 6>, v_{3} = <- 8, 4>, v_{4} = <10, 15>$
Which two vectors are orthogonal?