Question

Determine whether the given vectors are perpendicular.

Short answer

Vector u and v are perpendicular to each other where,

$\begin{array}{l}u=〈0,-5〉\\ v=〈4,0〉\end{array}$

Step-by-step solution

Step 1. Given information.

$\begin{array}{l}u=0i-5j\\ v=4i+0j\end{array}$

Step 2. Determining the dot product.

The dot product of vectors

$u·v=\left(0\right)\left(4\right)+(-5)\left(0\right)$

$u·v=0+0$

$u·v=0$

So the vectors u and v are perpendicular to each other.