SOLUTION: Hello Everyone please can you help with this a) Find a vector which is perpendicular to the plane containing the vectors a=6i+k and b=2i+j b) Find the area of the triangle wi

Algebra ->  Vectors -> SOLUTION: Hello Everyone please can you help with this a) Find a vector which is perpendicular to the plane containing the vectors a=6i+k and b=2i+j b) Find the area of the triangle wi      Log On


   

Question 368274: Hello Everyone please can you help with this
a) Find a vector which is perpendicular to the plane containing the vectors a=6i+k and b=2i+j
b) Find the area of the triangle with vertices at the points with coordinates (1,2,3),(4,-3,2) and (8,1,1)
Really wlould appreciate help on this one
Thanks
Mick
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) Use the cross product to find a vector perpendicular to both vector and the plane.
V=AxB
V=(6,0,1)x(2,1,0)
.
.
.
b) Again use the cross product
A:(1,2,3)
B:(4,-3,2)
C:(8,1,1)
Area=%281%2F2%29%28ABxAC%29
where AB is the vector from A to B and AC is the vector from A to C.
Check section 4.1 of http://en.wikipedia.org/wiki/Triangle for a derivation of this method.