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.i) which is r=d+λ(b−d) out of the list attatched ii) which is (a+b+c)/3 out of the list attatched is the distance from the point E to the plane Nis a vector equation for the line where M and N intersectis the distance from the point B to the point Eis a real number less than 0is the position vector of a point that lies on N but not on Mis the equation of the plane Mis a vector equation for a line that is contained in M but not in Nis the position vector of a point that lies on M but not on Nis the position vector for the midpoint of the line segment AEis the position vector of a point that lies neither on N nor on Mis a vector equation for a line that intersects M at exactly one pointis a meaningless expression

Answered: Image /qna-images/answer/3cee7dd5-1b62-4b50-bc2e-079b68bc58e4.jpg

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. i) which is r=d+λ(b−d) out of the list attatched ii) which is (a+b+c)/3 out of the list attatched

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. i) which is r=d+λ(b−d) out of the list attatched ii) which is (a+b+c)/3 out of the list attatched

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

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.

i) which is r=d+λ(b−d) out of the list attatched

ii) which is (a+b+c)/3 out of the list attatched

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

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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