The problem involves finding the set of points M such that the cross product of vectors AM and BC equals the cross product of vectors AM and AC. The context is centered around vector operations and their geometric interpretations.
The discussion is ongoing, with participants providing hints and exploring the geometric implications of the vectors involved. There is an emphasis on understanding the conditions under which the vectors are perpendicular, but no consensus or final conclusions have been reached regarding the set of points M can occupy.
Participants are navigating the concepts of vector cross products and their geometric interpretations, with some expressing uncertainty about the relationships between the vectors and the implications for point M's location.
If AM × BM = 0 , then how is AM oriented relative to BM ?Jeanclaud said:Find the set of points of M such that:
Homework Statement
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.
Right-handedSammyS said:If AM × BM = 0 , then how is AM oriented relative to BM ?
Do you mean that they form a right angle?Jeanclaud said:Right-handed
Thanks for the help.SammyS said: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.
To be sure that you fully understand:Jeanclaud said:Thanks for the help.