The cross product is the area of the parallelogram,
and so the area of the triangle is half that.

 

The area is ∥OQ×OR∥/2 =  = ∥-5i+7j-3k∥/2 =  

We find the magnitude of vectors OQ and OR

∥OQ∥ = 

∥OR∥ = 

-----------------------

ii) the projection of QR and OR

I think you meant "onto", not "and".

the projection of QR onto OR is given by

            OQ•OR
projOROQ  = ————— OR 
            ∥OR∥²

                          
OQ•OR = <1,2,3>•<2,1,-1> = (1)(2)+(2)(1)+(3)(-1) = 1

∥OR∥² = 2²+1²+(-1)² = 4+1+1 = 6

So,

projOROQ = 

Edwin