Position Vector Problem

[Felix]

Hi, I don't know how to solve the below vector problem. Help me please.


Vectors a, b, c are the position vectors for the points A, B, C respectively. ABCDEF is the regular hexagon. Find the position vectors for the points D, E, F in terms of a, b, c.

 

[Deleted member 4993]

Hi, I don't know how to solve the below vector problem. Help me please.


Vectors a, b, c are the position vectors for the points A, B, C respectively. ABCDEF is the regular hexagon. Find the position vectors for the points D, E, F in terms of a, b, c.

Position vectors are defined with respect to another (reference) point.

Where is/are the reference point/s?

 

[DrPhil]

Hi, I don't know how to solve the below vector problem. Help me please.


Vectors a, b, c are the position vectors for the points A, B, C respectively. ABCDEF is the regular hexagon. Find the position vectors for the points D, E, F in terms of a, b, c.

Position vectors are defined with respect to another (reference) point.

Where is/are the reference point/s?

You know you have a regular hexagon, but you don't know WHERE it is nor how it is oriented. I think it would be a good idea to find the radius of the hexagon, remembering that all the sides are equal and all the vertices are that same distance from the center of the hexagon. A hint (or two) to get you started:

......vector AB = b - a
......vector AC = c - a

The vector from B back toward the center of the hexagon is perpendicular to vector AC.