1. Vector product properties and are of quadrilateral

"Show, using vector algebra, that the area of a quadrilateral ABCD is given by 1/2|AC×BD| where AC and BD are the diagonals of ABCD."

I understand that in order to answer this question you split the quadrilateral into two triangles and use the formula "area of triangle = 1/2 |a x b|" but I don't understand how you get from the line "A =
1/2 |a×c+c×ba×c|" to "A=1/2 |c×b|" in the solutions attached. Surely in order for 'a x c' to be removed it should be '-a x -c' and not just '-a x c'.

2. Re: Vector product properties and are of quadrilateral

Originally Posted by ehendry91
"Show, using vector algebra, that the area of a quadrilateral ABCD is given by 1/2|AC×BD| where AC and BD are the diagonals of ABCD."
I understand that in order to answer this question you split the quadrilateral into two triangles and use the formula "area of triangle = 1/2 |a x b|" but I don't understand how you get from the line "A = 1/2 |a×c+c×b−a×c|" to "A=1/2 |c×b|" in the solutions attached. Surely in order for 'a x c' to be removed it should be '-a x -c' and not just '-a x c'.

Well $(a\times c)-(a\times c)=0$