Find the volume of the parallelepiped having vectors $a=(1,4,-7)$, $b=(2,-1,4)$, and $c=(0,-9,18)$ as adjacent edges. What conclusions can you make about vectors $a$,$b$, and $c$?
So to solve this I used the triple scalar product and got the equation $18i-144j-126k$ and the volume to be $192.1874$ units cubed. Is this correct? & What conclusions can I make about the vectors? I was thinking that $A$ and $B$ are orthogonal?
Best Answer
We use that $$V=|a\cdot ( b \times c)|=|(1,4,7)\cdot (18,-36,-18)|=0$$ This means the vectors are coplanar.