Can Geometry Help Solve This Vector Problem?

[mtayab1994]

Homework Statement

(E) is a group of points M from a level/plane

$$MA^{2}-MB^{2}=-4$$ 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 $$MA^{2}-MB^{2}=(MA-MB)(MA+MB)$$

then i got : $$MA^{2}-MB^{2}=BA*(MA+MB)$$

and i don't know where to go on from there any help?

 

[Mark44]

Homework Statement

(E) is a group of points M from a level/plane

$$MA^{2}+MB^{2}=-4$$ And I is the center of [AB]

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?

Homework Equations

show that IM*AB=-2 ( IM and AB have arrows on top)

The Attempt at a Solution

Well i split $$MA^{2}-MB^{2}=(MA-MB)(MA+MB)$$

then i got : $$MA^{2}-MB^{2}=BA*(MA+MB)$$

and i don't know where to go on from there any help?

 

[mtayab1994]

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?

My fault AB is a line segment and I is the center of it.

 

[SammyS]

Homework Statement

(E) is a group of points M from a level/plane

$$MA^{2}+MB^{2}=-4$$ And I is the center of [AB]
...

I think this is impossible! → $MA^{2}+MB^{2}=-4$

Do you mean? → $MA^{2}-MB^{2}=-4$

 

[mtayab1994]

I think this is impossible! → $MA^{2}+MB^{2}=-4$

Do you mean? → $MA^{2}-MB^{2}=-4$

Yea sorry my fault that was a typo its MA^2-MB^2=-4

 

[mtayab1994]

Any ideas?

 

[Mark44]

What does this mean?

show that IM*AB=-2 ( IM and AB have arrows on top)

Does * represent the dot product?

 

[mtayab1994]

What does this mean?

Does * represent the dot product?

Yes.

 

[SammyS]

Homework Statement

(E) is a group of points M from a level/plane

$$MA^{2}-MB^{2}=-4$$ 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 $$MA^{2}-MB^{2}=(MA-MB)(MA+MB)$$

then i got : $$MA^{2}-MB^{2}=BA*(MA+MB)$$

and i don't know where to go on from there any help?

My fault AB is a line segment and I is the center of it.

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, $\vec{MB}$ is a vector from point M to point B.

If that's the case, then notice that $\vec{MA}=\vec{MI}+\vec{IA}\,.$ Do similar for $\vec{MB}$

Notice that$\vec{IB}=-\vec{IA}\,.$

Now look at $\vec{MA}+\vec{MB}$ again.