Question

Check please, Linear Alg, Area of Parallelogram

P=(7,-5,5), Q=(-1,-2,8), R=(6,7,-2), S=(-2,10,1)

I got \(\vec{u}=(-8,3,3)\), \(\vec{v}=(1,-12,7)\), \(\vec{u}\times \vec{v}=57i+59j+93k\) Area = \(\sqrt{15379}\implies 13\sqrt{91}\)

Answer 1

I got \(\vec{u}=(-8,3,3)\), \(\vec{v}=(1,-12,7)\), \(\vec{u}\times \vec{v}=57i+59j+93k\)
Area = \(\sqrt{15379}\implies 13\sqrt{91}\)

Answer 2

Well the way you use is perfectly fine, you use the vector product to obtain the area of a parallelogram. So you basically want to verify the numeric answer? I usually put more empathizes on the actually math than the numeric solution, but if you want I can quickly double check.

Answer 3

I have all the math, I just want to see if my math is right. So I put in a few of th steps in case I have the wrong answer.

Answer 4

And it is such a cute little plane out there in 3d space!