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Show that if vER is a vector and that a ER is a real number, then vɅ(av) = 0

Show that if vER is a vector and that a ER is a real number, then vɅ(av) = 0

Advanced Engineering Mathematics
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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q2 Needed ASAP By hand solution needed for Q2 correctly in 30 minutes and get the thumbs up please show neat and clean work Please solve correctly
1. Find the equation of the plane that passes through the points (1,0,-1), (0,2,3) and (0,0,5) in R 2. Show that if VER is a vector and that a ER is a real number, then vɅ (av) = 0 3. Consider the whole: R = {(r, 0) |2 <r <3, π ≤0≤ 2π Draw R in the (r, 0) plane, write R in Cartesian coordinates x = r cos 0, y = r sin 0, and draw R in the (x, y) plane. 3 f 4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). f(x, y) = 2 2 5. Write the two-ply cone z = x + y in spherical coordinates (simplify its expression if possible). 6. Let A and B be two open subsets of R. Show that their intersection An B is also an open set. 7. Let the function f: R². R defined as follows xy² + 2x²y x² + 4y² 0 af si (x, y) = (0,0) si (x, y) = (0,0). af (1)
Transcribed Image Text:1. Find the equation of the plane that passes through the points (1,0,-1), (0,2,3) and (0,0,5) in R 2. Show that if VER is a vector and that a ER is a real number, then vɅ (av) = 0 3. Consider the whole: R = {(r, 0) |2 <r <3, π ≤0≤ 2π Draw R in the (r, 0) plane, write R in Cartesian coordinates x = r cos 0, y = r sin 0, and draw R in the (x, y) plane. 3 f 4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). f(x, y) = 2 2 5. Write the two-ply cone z = x + y in spherical coordinates (simplify its expression if possible). 6. Let A and B be two open subsets of R. Show that their intersection An B is also an open set. 7. Let the function f: R². R defined as follows xy² + 2x²y x² + 4y² 0 af si (x, y) = (0,0) si (x, y) = (0,0). af (1)
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