Chapter 10: Q. 76 (page 826)

Let u, v, and w be vectors in ${鈩�}^{3}$ . Prove that $u 路 (v 脳 w) = (u 脳 v) 路 w$ .
(This is part (b) of Theorem 10.37.)

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information

Let u, v and w be vectors in ${鈩�}^{3}$ . Prove that $u 路 (v 脳 w) = (u 脳 v) 路 w$ .

Step 2. Let u=(−3,1,−4), v=(2,0,5), and w=(1,3,13)

Now finding the value of $u 路 (v 脳 w)$

$u 路 (v 脳 w) = \det [\begin{matrix} - 3 & 1 & - 4 \\ 2 & 0 & 5 \\ 1 & 3 & 13 \end{matrix}] u 路 (v 脳 w) = - 3 |\begin{matrix} 0 & 5 \\ 3 & 13 \end{matrix}| - 1 |\begin{matrix} 2 & 5 \\ 1 & 13 \end{matrix}| - 4 |\begin{matrix} 2 & 0 \\ 1 & 3 \end{matrix}| u 路 (v 脳 w) = - 3 (0 脳 13 - 5 脳 3) - 1 (2 脳 13 - 5 脳 1) - 4 (2 脳 3 - 0 脳 1) u 路 (v 脳 w) = - 3 (0 - 15) - 1 (26 - 5) - 4 (6 - 0) u 路 (v 脳 w) = 45 - 21 - 24 u 路 (v 脳 w) = 0$

Step 3. Now finding the value of (u×v)·w

$(u 脳 v) 路 w = \det [\begin{matrix} - 3 & 1 & - 4 \\ 2 & 0 & 5 \\ 1 & 3 & 13 \end{matrix}] (u 脳 v) 路 w = - 3 |\begin{matrix} 0 & 5 \\ 3 & 13 \end{matrix}| - 1 |\begin{matrix} 2 & 5 \\ 1 & 13 \end{matrix}| - 4 |\begin{matrix} 2 & 0 \\ 1 & 3 \end{matrix}| (u 脳 v) 路 w = - 3 (0 脳 13 - 5 脳 3) - 1 (2 脳 13 - 5 脳 1) - 4 (2 脳 3 - 0 脳 1) (u 脳 v) 路 w = - 3 (0 - 15) - 1 (26 - 5) - 4 (6 - 0) (u 脳 v) 路 w = 45 - 21 - 24 (u 脳 v) 路 w = 0$

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

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91影视

Let u, v, and w be vectors in ${鈩�}^{3}$ . Prove that $u 路 (v 脳 w) = (u 脳 v) 路 w$ .
(This is part (b) of Theorem 10.37.)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let u=(−3,1,−4), v=(2,0,5), and w=(1,3,13)

Step 3. Now finding the value of (u×v)·w

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91影视

Let u, v, and w be vectors in 鈩�3. Prove that u路(v脳w)=(u脳v)路w.(This is part (b) of Theorem 10.37.)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let u=(−3,1,−4), v=(2,0,5), and w=(1,3,13)

Step 3. Now finding the value of (u×v)·w

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Applied Mathematics

Statistics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Let u, v, and w be vectors in ${鈩�}^{3}$ . Prove that $u 路 (v 脳 w) = (u 脳 v) 路 w$ .
(This is part (b) of Theorem 10.37.)