Finding points M where AM × BC = AM × AC

[Jeanclaud]

Homework Statement

Find the set of points of M such that:
AM x BC=AM x AC (Vectors)

The Attempt at a Solution

[/b]
AM x (BM+MC) =AMx(AM+MC)
AMxBM+AMxMC=AMxAM +AM x MC
Then AMxBM=0
MA X MB=0

I am new to this lesson and this is my first time i solve such a question and i had no idea how to solve it but i tried my best please some help give me some hints, Thank you.

 

[SammyS]

• Homework Statement

Find the set of points of M such that:
AM x BC=AM x AC (Vectors)

The Attempt at a Solution

AM x (BM+MC) =AMx(AM+MC)
AMxBM+AMxMC=AMxAM +AM x MC
Then AMxBM=0
MA X MB=0[/B]

I am new to this lesson and this is my first time i solve such a question and i had no idea how to solve it but i tried my best please some help give me some hints, Thank you.

If AM × BM = 0 , then how is AM oriented relative to BM ?

 

[Jeanclaud]

If AM × BM = 0 , then how is AM oriented relative to BM ?

Right-handed

 

[SammyS]

Right-handed

Do you mean that they form a right angle?

Yes, they do.

Look at two fixed points, A and B, in a plane. Consider where point M can lie, if vector, AM ⊥ BM . Now consider all such locations point M can occupy.

 

[Jeanclaud]

Do you mean that they form a right angle?

Yes, they do.

Look at two fixed points, A and B, in a plane. Consider where point M can lie, if vector, AM ⊥ BM . Now consider all such locations point M can occupy.

Thanks for the help.

 

[SammyS]

Thanks for the help.

To be sure that you fully understand:

What is your final conclusion regarding the set of points on which point M can lie?