Q. 69 Let u and v be vectors in 鈩�3. ... [FREE SOLUTION]

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Chapter 10: Q. 69 (page 825)

Let u and v be vectors in ${鈩�}^{3}$ . Prove that $v 路 (u 脳 v) = 0$ . (This is Theorem 10.31(b).)

Short Answer

Expert verified

Hence, we prove that $v 路 (u 脳 v) = 0$

Step by step solution

Step 1. Given Information

Let u and v be vectors in ${鈩�}^{3}$ . Prove that role="math" localid="1649924080419" $v 路 (u 脳 v) = 0$ .

Step 2. We have to prove v·(u×v)=0

Let $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$

Now the determinant is

$v 路 (u 脳 v) = \det [\begin{matrix} v_{1} & v_{2} & v_{3} \\ u_{1} & u_{2} & u_{3} \\ v_{1} & v_{2} & v_{3} \end{matrix}] v 路 (u 脳 v) = v_{1} |\begin{matrix} u_{2} & u_{3} \\ v_{2} & v_{3} \end{matrix}| - v_{2} |\begin{matrix} u_{1} & u_{3} \\ v_{1} & v_{3} \end{matrix}| + v_{3} |\begin{matrix} u_{1} & u_{2} \\ v_{1} & v_{2} \end{matrix}| v 路 (u 脳 v) = v_{1} (u_{2} v_{3} - u_{3} v_{2}) - v_{2} (u_{1} v_{3} - u_{3} v_{1}) + v_{3} (u_{1} v_{2} - u_{2} v_{1}) v 路 (u 脳 v) = v_{1} u_{2} v_{3} - v_{1} u_{3} v_{2} - v_{2} u_{1} v_{3} + v_{2} u_{3} v_{1} + v_{3} u_{1} v_{2} - v_{3} u_{2} v_{1} v 路 (u 脳 v) = 0$

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91影视

Let u and v be vectors in ${鈩�}^{3}$ . Prove that $v 路 (u 脳 v) = 0$ . (This is Theorem 10.31(b).)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We have to prove v·(u×v)=0

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91影视

Let u and v be vectors in 鈩�3. Prove that v路(u脳v)=0. (This is Theorem 10.31(b).)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We have to prove v·(u×v)=0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Pure Maths

Probability and Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Let u and v be vectors in ${鈩�}^{3}$ . Prove that $v 路 (u 脳 v) = 0$ . (This is Theorem 10.31(b).)