Please help finding the area and volume dealing with vectors?

1.Find the area of the triangle with vertices at P(1,3,-2), Q(2,4,5) and R(-3,-2,2) ? ?





shall i use the cross product ? ?





2. Find the volume of a parallelopiped with adjacent edges OP,OQ and OR when P(1,1,0), O(1,0,1) amd R(0,1,1)


shall i use this I A dot product CB cross product C I,how will i use this





thanks for helping me ! ! !

Please help finding the area and volume dealing with vectors?
Aquavires is correct
Reply:Yep, you're right... since you're dealing with vectors, the dot product and cross product are your only options I think. =) I'm assuming that you already know how to find dot and cross products. If you don't, just let me know and I'll be glad to explain in more detail.





1. When you calculate |PQ cross PR|, you will get


the area of a parallelogram PQSR


(S is opposite to P, Q is opposite to R)


where PQ=RS and PR=QS.





To find the area of your triangle, just halve the result of |PQ cross PR|.


This is because when you draw a line QR, you will divide the parallelogram PQSR into 2 equal triangles.





2. The formula is Volume = | A dot (B cross C) |


i.e. find the answer of (B cross C) first,


then find (A dot [answer]).


It doesn't matter whether you let A be OP, OQ or OR. The final result will be the same.





Hope this helps. If my words are too confusing, grab a pen and paper and draw the parallelogram I described... it might help. The 2 Wikipedia links might also be useful.





Good luck!