Chapter 10: Q. 20 (page 824)

If u, v, and ware three mutually orthogonal vectors in $ℝ^{3}$ , explain why $u \times (v \times w) = 0$ .

Short Answer

Expert verified

$u \times (v \times w) = 0$ because $u \times (v \times w) = (u \cdot w) v - (u \cdot v) w$ andu, v, and ware three mutually orthogonal vectors.

Step by step solution

Step 1. Given Information

If u, v, and ware three mutually orthogonal vectors in $ℝ^{3}$ , explain why $u \times (v \times w) = 0$ .

Step 2. It is given that u, v, and w are three mutually orthogonal vectors in ℝ3.

As we know that $u \times (v \times w) = (u \cdot w) v - (u \cdot v) w$

Since u, v, and ware three mutually orthogonal so the $u \cdot w and u \cdot v$ is zero.

$u \times (v \times w) = 0 \times v - 0 \times w u \times (v \times w) = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If u, v, and ware three mutually orthogonal vectors in $ℝ^{3}$ , explain why $u \times (v \times w) = 0$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. It is given that u, v, and w are three mutually orthogonal vectors in ℝ3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If u, v, and ware three mutually orthogonal vectors in ℝ3, explain why u×(v×w)=0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. It is given that u, v, and w are three mutually orthogonal vectors in ℝ3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If u, v, and ware three mutually orthogonal vectors in $ℝ^{3}$ , explain why $u \times (v \times w) = 0$ .