Chapter 10: Q. 74 (page 826)

Let u, v, andw be vectors in ${鈩�}^{3}$ . Prove that $u 脳 v = u 脳 w$ if and only if u is parallel to $v 鈭� w$ .

Short Answer

Expert verified

Hence, we prove that $u 脳 v = u 脳 w$ if and only if u is parallel to $v - w$ .

Step by step solution

Step 1. Given Information

Let u, v, and w be vectors in ${鈩�}^{3}$ . Prove that $u 脳 v = u 脳 w$ if and only if u is parallel to $v 鈭� w$ .

Step 2. Let u, v, and w be vectors in ℝ3.

$u 脳 v = u 脳 w Subtract u 脳 w on both side u 脳 v - u 脳 w = u 脳 w - u 脳 w u 脳 v - u 脳 w = 0 u 脳 (v - w) = 0 u = 0 v - w = 0$

That means $u 鈭� v - w$ .

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91影视

Let u, v, andw be vectors in ${鈩�}^{3}$ . Prove that $u 脳 v = u 脳 w$ if and only if u is parallel to $v 鈭� w$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let u, v, and w be vectors in ℝ3.

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91影视

Let u, v, andw be vectors in 鈩�3. Prove that u脳v=u脳wif and only if u is parallel to v鈭�w.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let u, v, and w be vectors in ℝ3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Pure Maths

Calculus

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Let u, v, andw be vectors in ${鈩�}^{3}$ . Prove that $u 脳 v = u 脳 w$ if and only if u is parallel to $v 鈭� w$ .