Question

Find a vector orthogonal to both \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Short answer

The orthogonal vector is \((5i-4j-6k)\).

Step-by-step solution

Given Information

The given vectors are \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Let the orthogonal vector be \(b\).

\(b=u\times v\).

Find the orthogonal vector

The vector is,

\(\begin{align*}\vec{b}&= \begin{vmatrix}i&j&k\\2&4&-1\\0&-3&2\end{vmatrix}\\&=5i-4j-6k\end{align*}\)