Is the Sine Rule Valid for Non-Triangular Vector Configurations?

[Krushnaraj Pandya]

Homework Statement

If magnitudes of vector a,b and c are 1,2,3 respectively and vectors a+b+c=0 then it is obvious that a and b will be in the opposite direction to c therefore cancelling it out but let's assume for a moment that we don't know this and we want to figure this out using the sine rule- then x/3 = y/2 = z/1 where z is the angle between b and c (opposite to a), x is the angle between a and b; and so on, also x+y+z=2pi from the figure (like three forces in equilibrium)-solving gives x equal to sixty degrees which is incorrect.

Is the sine rule obeyed only when the vectors form a triangle then?

Homework Equations

All relevant mentioned above

The Attempt at a Solution

Stated above

 

[Doc Al]

then x/3 = y/2 = z/1

You forgot to take the sine of the angles.

 

[Krushnaraj Pandya]

oh god, this is what happens when I study math all day. Thank you very much for your patience and help

 

[Doc Al]

I know the feeling!