Chapter 10: Q. 19 (page 824)

If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u and v?

Short Answer

Expert verified

$u \cdot v = 0 and u \times v = 0$ concluded that at least one of them is $0$ .

Step by step solution

Step 1. Given Information

If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u andv?

Step 2. If u and v are vectors in ℝ3 such that u·v=0 and u×v=0.

$u \cdot v = 0$ if vectors u and v are orthogonal.

The cross product $u \times v = 0$ is u and v are parallel.

Now we can also say that $u \cdot v = 0 and u \times v = 0$ concluded that at least one of them is $0$ .

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If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u and v?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. If u and v are vectors in ℝ3 such that u·v=0 and u×v=0.

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If u and v are vectors in ℝ3 such that u·v=0 and u×v=0, what can we conclude about u and v?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. If u and v are vectors in ℝ3 such that u·v=0 and u×v=0.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Logic and Functions

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u and v?