Question

Determine whether the given vectors are perpendicular.

$u=2i,v=-7j$

Short answer

Vector u and v are perpendicular to each other where,

$\begin{array}{l}u=2i\\ v=7j\end{array}$

Step-by-step solution

Step 1. Given information.

$\begin{array}{l}u=2i+0j\\ v=0i-7j\end{array}$

Step 2. Determining the dot product.

The dot product of vectors

$u·v=\left(2\right)\left(0\right)+\left(0\right)(-7)$

$u·v=0+0$

$u·v=0$

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