Chapter 10: Q. 14 (page 824)

What is the definition of the triple scalar product for vectors u, v and w in $ℝ^{3}$ ?

Short Answer

Expert verified

The triple scalar product is $u \cdot (v \times w) = v \cdot (w \times u) = w \cdot (u \times v)$ .

Step by step solution

Step 1. Given Information

We have to define the definition of the triple scalar product for vectors u, v and w in $ℝ^{3}$ .

Step 2. The definition of the triple scalar product

Let u, v and w be three vectors in $ℝ^{3}$ . The triple scalar product is $u \cdot (v \times w) = v \cdot (w \times u) = w \cdot (u \times v)$ . The triple scalar product is the signed volume of the parallelepiped formed using the three vectors, u, v and w.

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What is the definition of the triple scalar product for vectors u, v and w in $ℝ^{3}$ ?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The definition of the triple scalar product

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What is the definition of the triple scalar product for vectors u, v and w in ℝ3?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The definition of the triple scalar product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

What is the definition of the triple scalar product for vectors u, v and w in $ℝ^{3}$ ?