Here is a new Maths question for 2013.

ABC is a triangle of forces.

Prove that the magnitude of the resultant vector which consists of the sum of AB, 2*BC and 3*CA is the square root of b²+c²+2bc.cos(A) and that its direction is that of the diagonal through A of the parallelogram of which AB abd AC are adjacent sides.

Notes:

1) The vectors AB,BC, and CA should have either bars or arrows above the letters to denote their vectorial properties.

2) a,b,c represent the triangles sides opposite the angles at A,B and C as per convention.

And a happy new year to all!

and extending it once in the AB direction and twice in the AC direction,

We can start at the corner opposite to A of the parallelogram of which AB abd AC are adjacent sides (A+AB+AC)

From there, go to A+AB+AC+AB to A+AB+AC+AB+2BC to A+AB+AC+AB+2BC+3CA

and you will find yourself back at A, the other end of the diagonal.

The length of the diagonal is b²+c²+2bc.cos(A)