Please solve part f and g correctly and handwritten

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
icon
Related questions
Question
Please solve part f and g correctly and handwritten
2. Demonstrate the following relationship involving the dot product and cross product
(a) u. (v xw) = v. (w × u) = w · (u x V)
(b) u. (u x v)
=
0
(and explain geometrically why the result is zero)
(c) (a × b) × (a × c) = [(a × b) · c]a
.
(d) (a × b) · (c × d)
=
(a · c) (b · d) — (b · c) (a · d)
(e) a × (b × c) + cx (a × b) + b × (c × a) = 0
(f) ||a+b|| ≤ ||a|| + ||b||
(g) (a · b)² + ||a × b||² = ||a||²||b||².
Transcribed Image Text:2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw) = v. (w × u) = w · (u x V) (b) u. (u x v) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a . (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b|| (g) (a · b)² + ||a × b||² = ||a||²||b||².
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning