Q. 12 Give an example of three vectors... [FREE SOLUTION]

Chapter 10: Q. 12 (page 824)

Give an example of three vectors in ${鈩�}^{3}$ that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

Short Answer

Expert verified

The example of a right-handed triple is $i, j, k$ .

The same three vectors form a left-handed triple if W lies on the side of the plane through O, U, V does not indicated by your second [middle] finger.

Step by step solution

Step 1. Given Information

Give an example of three vectors in ${鈩�}^{3}$ that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

Step 2. Right-handed and left-handed triples

Suppose now that u, v, w are not coplanar. Pick an origin $O$ in 3-space, and define U, V , W by the condition that $\overset{鈫�}{O U}, \overset{鈫�}{O V}, \overset{鈫�}{O W}$ represent u, v, w respectively. Using your right hand put your thumb in the direction of u, and your first [index] finger in the direction of v.

Step 3. If W lies on the side of the plane through O, U, V indicated by your second [middle] finger, we call u, v, w a right-handed triple; otherwise it is a left-handed triple.

The example of a right-handed triple is $i, j, k .$

The same three vectors form a left-handed triple if W lies on the side of the plane through O, U, V does not indicated by your second [middle] finger.

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91影视

Give an example of three vectors in ${鈩�}^{3}$ that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Right-handed and left-handed triples

Step 3. If W lies on the side of the plane through O, U, V indicated by your second [middle] finger, we call u, v, w a right-handed triple; otherwise it is a left-handed triple.

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91影视

Give an example of three vectors in 鈩�3that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Right-handed and left-handed triples

Step 3. If W lies on the side of the plane through O, U, V indicated by your second [middle] finger, we call u, v, w a right-handed triple; otherwise it is a left-handed triple.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Give an example of three vectors in ${鈩�}^{3}$ that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.