The Cross Product: Suppose that u = (u1, u2, u3 ) and v = (v1, V2, V3 ) are from R³. Let us define the vector: 4. ủ xỹ = (u2v3 – uzv2)i – (u1V3 – uzv1)j+ (u¡v2 – uzv1)k, 3V2 - U3V1 called the cross product of ủ and i, pronounced i cross v. Section 2.4 The Dot Product and Orthogonality Warm-up: Let i = (7,–5, 2), and i = (8, 2,–3). Find ū xi and v x u. b. Find u o (u x v) and vo (ủ x i) for the vectors in (a). What can you conclude? Prove in general that for any ủ, v e R3: ủ x v is orthogonal to both ủ and v. а. с. This magical property of the cross product will be useful in succeeding problems.
The Cross Product: Suppose that u = (u1, u2, u3 ) and v = (v1, V2, V3 ) are from R³. Let us define the vector: 4. ủ xỹ = (u2v3 – uzv2)i – (u1V3 – uzv1)j+ (u¡v2 – uzv1)k, 3V2 - U3V1 called the cross product of ủ and i, pronounced i cross v. Section 2.4 The Dot Product and Orthogonality Warm-up: Let i = (7,–5, 2), and i = (8, 2,–3). Find ū xi and v x u. b. Find u o (u x v) and vo (ủ x i) for the vectors in (a). What can you conclude? Prove in general that for any ủ, v e R3: ủ x v is orthogonal to both ủ and v. а. с. This magical property of the cross product will be useful in succeeding problems.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
2.4 #4
The questions are in the picture
Please answer a, b, and c
Transcribed Image Text:The Cross Product: Suppose that u = (u1, u2, u3 ) and v = (v1, v2, V3 ) are from R³.
Let us define the vector:
4.
ủ xỉ = (uzv3 – uzv2)i – (u¡V3 – uzv1)j+ (u1v2 – uzv1)k,
called the cross product of ủ and v, pronounced i cross
Section 2.4 The Dot Product and Orthogonality
165
Warm-up: Let ủ = (7,–5, 2), and v = (8, 2,–3). Find ủ × v and v ×ủ.
Find u o (u x v) and vo (ủ × v) for the vectors in (a). What can you conclude?
Prove in general that for any u, v e R3: i ×v is orthogonal to both ỉ and v.
This magical property of the cross product will be useful in succeeding problems.
а.
b.
с.
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