Chapter 10: Q. 15 (page 824)

If the triple scalar product $u \cdot (v \times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Short Answer

Expert verified

The triple scalar product $u \cdot (v \times w)$ is equal to zero if and only if u, v and ware coplanar.

Step by step solution

Step 1. Given Information

If the triple scalar product $u \cdot (v \times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Step 2.We have to find the relationship do the vectors u, v and w have if the triple scalar product u·(v×w) is equal to zero.

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

The triple scalar product $u \cdot (v \times w)$ is equal to zero if and only if u, v andware coplanar.

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If the triple scalar product $u \cdot (v \times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Short Answer

Step by step solution

Step 1. Given Information

Step 2.We have to find the relationship do the vectors u, v and w have if the triple scalar product u·(v×w) is equal to zero.

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If the triple scalar product u·(v×w) is equal to zero, what geometric relationship do the vectors u, v and w have?

Short Answer

Step by step solution

Step 1. Given Information

Step 2.We have to find the relationship do the vectors u, v and w have if the triple scalar product u·(v×w) is equal to zero.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Logic and Functions

Pure Maths

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

If the triple scalar product $u \cdot (v \times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?