Question

Compute the area of the parallelogram determined by \(u\) and \(v\) where \(u=i\) and \(v=2j\).

Short answer

The area of a parallelogram is \(2\) sq units.

Step-by-step solution

Given Information

The two vectors are \(u=i\) and \(v=2j\).

Area of parallelogram \(=|u\times v|\).

Find the area of a parallelogram

\(\text{Area }=\begin{vmatrix}i&j&k\\1&0&0\\0&2&0\end{vmatrix}\)

\(\text{Area }=|0i+0j+2k|\)

\(\text{Area }=2\)