is the distance from the point E to the plane N is a vector equation for the line where M and N intersect is the distance from the point B to the point E is a real number less than 0 is the position vector of a point that lies on N but not on M is the equation of the plane M is a vector equation for a line that is contained in M but not in N is the position vector of a point that lies on M but not on N is the position vector for the midpoint of the line segment AE is the position vector of a point that lies neither on N nor on M is a vector equation for a line that intersects M at exactly one point is a meaningless expression
is the distance from the point E to the plane N is a vector equation for the line where M and N intersect is the distance from the point B to the point E is a real number less than 0 is the position vector of a point that lies on N but not on M is the equation of the plane M is a vector equation for a line that is contained in M but not in N is the position vector of a point that lies on M but not on N is the position vector for the midpoint of the line segment AE is the position vector of a point that lies neither on N nor on M is a vector equation for a line that intersects M at exactly one point is a meaningless expression
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
This is a long question i dont mind if this can somehow be counted as multiple questions
Let A, B, C, D be distinct points in 3-space with position vectors a, b, c, d respectively. Let E be the midpoint of the line segment AC.
Let M be the plane passing through the three points A,B,C and let N be the plane passing through the three points A,C,D. Assume that the points are chosen so that M and N are distinct, well-defined planes.
There is a list of expressions/equations attatched and they need to be matched to their values which are also attatched.
Transcribed Image Text:is the distance from the point E to the plane N
is a vector equation for the line where M and N intersect
is the distance from the point B to the point E
is a real number less than 0
is the position vector of a point that lies on N but not on M
is the equation of the plane M
is a vector equation for a line that is contained in M but not in N
is the position vector of a point that lies on M but not on N
is the position vector for the midpoint of the line segment AE
is the position vector of a point that lies neither on N nor on M
is a vector equation for a line that intersects M at exactly one point
is a meaningless expression
Transcribed Image Text:r = d + X(b - d)
atbte
3
2b-a-c
2
r = a+ X(c-a)
r = a+ X(b-a)
b+d
2
a+d
2
((b-a) × (c-a)) + a·d
3a+c
4
0
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