Question
Find the area of a triangle formed by vectors 𝑥⃗ and 𝑦⃗, if 𝑥⃗ = $\vec {A}+2\vec {B}$, 𝑦⃗ = $2\vec {A} – \vec {B}$ where |$\vec {A}$| = 3, |$\vec {B}$| = 4, and the angle between $\vec {A}$ and $\vec {B}$ is π/6
I can't figure out how to find it without vectors components.
Best Answer
The area is $$Ar=\frac{1}{2} |\vec x \times \vec y|= \frac{1}{2}|(\vec A +2 \vec B) \times (2\vec A- \vec B)]|= \frac{1}{2}|2 \vec B \times \vec A -\vec A \times \vec B]|=\frac{3}{2} |\vec A \times \vec B| =\frac{3}{2} |A||B| |\hat n|\sin(\pi/6)= 9 $$
Here we have used $\vec A \times \vec A=0$, $\vec A \times \vec B=-\vec B \times \vec A$ and that $|\hat n|=1$.