The discussion revolves around a vector problem involving points M, A, and B in a plane, where the relationship between the distances from M to A and B is expressed through the equation MA² - MB² = -4. Participants are tasked with showing that the product of vectors IM and AB equals -2, with I being the midpoint of segment AB.
The discussion is ongoing, with participants clarifying the problem statement and addressing typographical errors. Some have provided insights into vector relationships, while others are still seeking clarity on the problem's requirements and notation.
There is confusion regarding the initial conditions of the problem, particularly the equation involving MA² and MB², which was initially misstated. Participants are also navigating the implications of vector notation and the geometric interpretation of the problem.
This doesn't make any sense to me.mtayab1994 said:Homework Statement
(E) is a group of points M from a level/plane
[tex]MA^{2}+MB^{2}=-4[/tex] And I is the center of [AB]
mtayab1994 said:Homework Equations
show that IM*AB=-2 ( IM and AB have arrows on top)
The Attempt at a Solution
Well i split [tex]MA^{2}-MB^{2}=(MA-MB)(MA+MB)[/tex]
then i got : [tex]MA^{2}-MB^{2}=BA*(MA+MB)[/tex]
and i don't know where to go on from there any help?
Mark44 said:This doesn't make any sense to me.
What is A? What is B? Is AB the line segment from point A to point B?
I think this is impossible! → [itex]MA^{2}+MB^{2}=-4[/itex]mtayab1994 said:Homework Statement
(E) is a group of points M from a level/plane
[tex]MA^{2}+MB^{2}=-4[/tex] And I is the center of [AB]
...
SammyS said:I think this is impossible! → [itex]MA^{2}+MB^{2}=-4[/itex]
Do you mean? → [itex]MA^{2}-MB^{2}=-4[/itex]
Does * represent the dot product?mtayab1994 said:show that IM*AB=-2 ( IM and AB have arrows on top)
Mark44 said:What does this mean?
Does * represent the dot product?
mtayab1994 said:Homework Statement
(E) is a group of points M from a level/plane
[tex]MA^{2}-MB^{2}=-4[/tex] And I is the center of [AB]
Homework Equations
show that IM*AB=-2 ( IM and AB have arrows on top)
The Attempt at a Solution
Well i split [tex]MA^{2}-MB^{2}=(MA-MB)(MA+MB)[/tex]
then i got : [tex]MA^{2}-MB^{2}=BA*(MA+MB)[/tex]
and i don't know where to go on from there any help?
Since "IM and AB have arrows on top", and "AB is a line segment", I take it that these are all vectors and, for example, [itex]\vec{MB}[/itex] is a vector from point M to point B.mtayab1994 said:My fault AB is a line segment and I is the center of it.