Question

Find the area of the parallelogram determined by \(u=2i+4j-k\) and \(v=-3j+2k\).

Short answer

The area is \(\sqrt{77}\) sq units.

Step-by-step solution

Given Information

The given vectors are \(u=2i+4j-k\) and \(v=-3j+2k\).

The area of the parallelogram is \(|u\times v|\).

Calculate the area of parallelogram

\(\begin{align*}\text{Area }&=\left | \begin{vmatrix}i&j&k\\2&4&-1\\0&-3&2\end{vmatrix}\right |\\&=|5i-4j-6k|\\&=\sqrt{5^2+(-4)^2+(-6)^2}\\&=\sqrt{25+16+36}\\&=\sqrt{77}\end{align*}\)