Chapter 10: Q. 21 (page 824)

If u and v are vectors in $ℝ^{3}$ such that $u \times v = v \times u$ , what can we conclude about u and v?

Short Answer

Expert verified

We conclude about u and v that they are parallel.

Step by step solution

Step 1. Given Information

If u and v are vectors in $ℝ^{3}$ such that $u \times v = v \times u$ , what can we conclude about u andv?

Step 2. We conclude about u and v:

The cross product may be the first product you’ve encountered that is not commutative. However, it is anti-commutative. That is, for every two vectors u and v in $ℝ^{3}$ , we have the following:

$v \times u = u \times v$

We conclude about u and vthat they are parallel.

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If u and v are vectors in $ℝ^{3}$ such that $u \times v = v \times u$ , what can we conclude about u and v?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We conclude about u and v:

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If u and v are vectors in ℝ3 such that u×v=v×u, what can we conclude about u and v?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We conclude about u and v:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

If u and v are vectors in $ℝ^{3}$ such that $u \times v = v \times u$ , what can we conclude about u and v?