6. Complete the following for plane with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6). A. Write an equation of plane as ax + by + cz = d where a, b, c, and d are integers. B. Sketch the plane in the first octant of a right hand system. C. Find the point on the plane that is closest to the origin. D. Calculate the surface area of the triangular region formed by the intersection of the
6. Complete the following for plane with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6). A. Write an equation of plane as ax + by + cz = d where a, b, c, and d are integers. B. Sketch the plane in the first octant of a right hand system. C. Find the point on the plane that is closest to the origin. D. Calculate the surface area of the triangular region formed by the intersection of the
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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Transcribed Image Text:6. Complete the following for plane
A. Write an equation of plane
B. Sketch the plane in the first octant of a right hand system.
C. Find the point on the plane that is closest to the origin.
D. Calculate the surface area of the triangular region formed by the intersection of the
plane with the coordinate axis planes.
with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6).
as ax + by + cz = d where a, b, c, and d are integers.
E. Calculate the volume of the tetrahedron formed by the intersection of the plane with
the coordinate axis planes.
F. Use Green's Theorem to calculate the circulation in the presence of F(-y², x) around
the triangular region in the xy-plane region formed the intersection of the plane with
the coordinate axis planes. That is, set D is the triangle with vertices at the origin, P(3,
0), and Q(0, 2).
G. Use Green's Theorem to calculate the flux of F = (-y2, x) with upward pointing normal
vector through the triangular region in the xy-plane region formed the intersection of
the plane with the coordinate axis planes. That is, set D is the triangle with vertices at
the origin, P(3, 0), and Q(0, 2).
H. Calculate the circulation in the presence of the field = (-y, x, z) around the curve C:
the triangular region formed by the intersection of the plane with the coordinate axis
planes using Stoke's Theorem:
S
I. Use the Divergence Theorem:
7x F. ds =
D
VXF ñ dA.
ff # · ds = fff
S
E
7. F dv
to calculate the flux of the field = (-y, x, z) through the tetrahedron formed by the
intersection of plane & the with the coordinate axis planes.
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