Q. 79 Prove that if vectors r, s, u, a... [FREE SOLUTION]

Chapter 10: Q. 79 (page 826)

Prove that if vectors r, s, u, and v in ${鈩�}^{3}$ can all be translated to the same plane, thenrole="math" localid="1650041930138" $(r 脳 s) 脳 (u 脳 v) = 0$

Short Answer

Expert verified

Hence, prove that $(r 脳 s) 脳 (u 脳 v) = 0$

Step by step solution

Step 1. Given Information

Prove that if vectors r, s, u, and v in ${鈩�}^{3}$ can all be translated to the same plane, then $(r 脳 s) 脳 (u 脳 v) = 0$

Step 2. As we know that "The cross product of two parallel vectors u and v in ℝ3 is u×v=0.

Hence, $r 脳 s = 0$ when r and sare parallel vectors.

Also $u 脳 v = 0$ when u and vare parallel vectors.

Now we can say that

If r, s, u, and v all lie in some plane P, then the cross products $r 脳 s$ and $u 脳 v$ are both orthogonal to P. Therefore, these two vectors are parallel and the cross product of two parallel vectors is $0$ .

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91影视

Prove that if vectors r, s, u, and v in ${鈩�}^{3}$ can all be translated to the same plane, thenrole="math" localid="1650041930138" $(r 脳 s) 脳 (u 脳 v) = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. As we know that "The cross product of two parallel vectors u and v in ℝ3 is u×v=0.

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91影视

Prove that if vectors r, s, u, and v in 鈩�3 can all be translated to the same plane, thenrole="math" localid="1650041930138" (r脳s)脳(u脳v)=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. As we know that "The cross product of two parallel vectors u and v in ℝ3 is u×v=0.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Pure Maths

Discrete Mathematics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Prove that if vectors r, s, u, and v in ${鈩�}^{3}$ can all be translated to the same plane, thenrole="math" localid="1650041930138" $(r 脳 s) 脳 (u 脳 v) = 0$