Q. 73 Let u and v be vectors in 鈩�3 s... [FREE SOLUTION]

Chapter 10: Q. 73 (page 826)

Let u and v be vectors in ${鈩�}^{3}$ such that $u 路 v = 0$ . Prove that if $胃$ is the angle between u and v, then role="math" localid="1650011942678" $\tan 胃 = \frac{||u 脳 v||}{u 路 v}$

Short Answer

Expert verified

Hence, we prove that if $胃$ is the angle between u and v, then $\tan 胃 = \frac{||u 脳 v||}{u 路 v}$

Step by step solution

Step 1. Given Information

Let u and v be vectors in ${鈩�}^{3}$ such that $u 路 v = 0$ . Prove that if $胃$ is the angle between u and v, then $\tan 胃 = \frac{||u 脳 v||}{u 路 v}$

Step 2. As we know that if u, v, and u × v form a right-handed triple.

Then, $||u 脳 v|| = ||u|| ||v|| \sin 胃鈥� 鈥� 鈥� 鈥� Equation 1$

u, v, and $u 路 v$ form a left-handed triple.

role="math" localid="1650014121047" $u 路 v = ||u|| ||v|| \cos 胃鈥� 鈥� 鈥� 鈥� Equation 2$

Step 3. Divide the equation 1 and 2

$\frac{||u 脳 v||}{u 路 v} = \frac{||u|| ||v|| \sin 胃}{||u|| ||v|| \cos 胃} \frac{||u 脳 v||}{u 路 v} = \frac{\sin 胃}{\cos 胃} \frac{||u 脳 v||}{u 路 v} = \tan 胃 \tan 胃 = \frac{||u 脳 v||}{u 路 v}$

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91影视

Let u and v be vectors in ${鈩�}^{3}$ such that $u 路 v = 0$ . Prove that if $胃$ is the angle between u and v, then role="math" localid="1650011942678" $\tan 胃 = \frac{||u 脳 v||}{u 路 v}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. As we know that if u, v, and u × v form a right-handed triple.

Step 3. Divide the equation 1 and 2

One App. One Place for Learning.

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91影视

Let u and v be vectors in 鈩�3 such that u路v=0. Prove that if 胃 is the angle between u and v, then role="math" localid="1650011942678" tan胃=u脳vu路v

Short Answer

Step by step solution

Step 1. Given Information

Step 2. As we know that if u, v, and u × v form a right-handed triple.

Step 3. Divide the equation 1 and 2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Let u and v be vectors in ${鈩�}^{3}$ such that $u 路 v = 0$ . Prove that if $胃$ is the angle between u and v, then role="math" localid="1650011942678" $\tan 胃 = \frac{||u 脳 v||}{u 路 v}$