Q50E If聽u鈫�,v鈫�,w鈫捖燼re three un... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q50E (page 276)

If $\overset{鈫�}{u}, \overset{鈫�}{v}, \overset{鈫�}{w}$ are three unit vectors in ${鈩�}^{3}$ , what are the possible values of $d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}]$ ?

Short Answer

Expert verified

Therefore, the possible values of $d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}]$ is given by,

$d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}] 鈭� [- 1, 1]$

Step by step solution

Given.

Consider, the given unit vector,

Unit Vectors $= \overset{鈫�}{u}, \overset{鈫�}{v}, \overset{鈫�}{w}$ .

To find the possible value of det[u→v→w→].

If $\overset{鈫�}{u}, \overset{鈫�}{v}, \overset{鈫�}{w}$ are unit vectors, then

$d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}] = (\overset{鈫�}{u} 脳 \overset{鈫�}{v} 脳 \overset{鈫�}{w})$

Since $\overset{鈫�}{u}$ and $\overset{鈫�}{v}$ are unit vectors, then $\overset{鈫�}{u} 脳 \overset{鈫�}{v}$ is also a unit vector. If $蠁$ is the angle between $\overset{鈫�}{u} 脳 \overset{鈫�}{v}$ and $\overset{鈫�}{w}$ , then

$\cos 蠁 = \frac{(\overset{鈫�}{u} 脳 \overset{鈫�}{v} 脳 \overset{鈫�}{w})}{||\overset{鈫�}{u} 脳 \overset{鈫�}{v}|| ||\overset{鈫�}{w}||} = (\overset{鈫�}{u} 脳 \overset{鈫�}{v} 脳 \overset{鈫�}{w}) = d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}]$ , which means that the right side of this equation can vary between -1 and 1.

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91影视

If $\overset{鈫�}{u}, \overset{鈫�}{v}, \overset{鈫�}{w}$ are three unit vectors in ${鈩�}^{3}$ , what are the possible values of $d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}]$ ?

Short Answer

Step by step solution

Given.

To find the possible value of det[u→v→w→].

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91影视

Ifu鈫�,v鈫�,w鈫�are three unit vectors in鈩�3, what are the possible values ofdet[u鈫�v鈫�w鈫�]?

Short Answer

Step by step solution

Given.

To find the possible value of det[u→v→w→].

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Decision Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

If $\overset{鈫�}{u}, \overset{鈫�}{v}, \overset{鈫�}{w}$ are three unit vectors in ${鈩�}^{3}$ , what are the possible values of $d e t [\begin{matrix} \overset{鈫�}{u} & \overset{鈫�}{v} & \overset{鈫�}{w} \end{matrix}]$ ?