area of triangle using vector

Apr 2014
275
1
canada
pls refer to part b , i cant understand the ans provided.

can i use 0.5| OP x OS| or 0.5|OP x OR | to find the ans? instead of 0.5|OR x OS| vector.pngvector ans.png
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
It can be shown that if A and B are vectors giving two non-parallel sides of a parallelogram, then |A x B| is the area of the parallelogram. Since we can always think of a triangle as half of a parallelogram, the area of a triangle, with sides given by vectors A and B, is 1/2 |A x B|.

HOWEVER, here, OP, OR, and OS are NOT the sides of this triangle so NONE of the formulas you give are correct. The vector PR= OP- OR is a side of the triangle.