vectors and the area of parallelogram

Question

On vectors $a = 14i -2j +5k$ and $b = -2i+6j-11k$ is parallelogram. Calculate its area. My idea is to find cross product $a \times b = (-8 , -144, 80)$ and the compute lenght of this vector , it is $\sqrt{8^2 + (-144)^2 + 80^2} = 40* \sqrt{17}$ . IS it correct?

Answer 1

Hint: The area of a parallelogram can computed as $$A=|\vec{a}\times \vec{b}|$$ the so-called cross product. I got $$\vec{a}\times \vec{b}=<-8,144,80>$$