Question

Determine whether the given vectors are perpendicular.

$u=4i,v=-i+3j$

Short answer

Vector u and v are not perpendicular to each other where,

$\begin{array}{l}u=4i\\ v=-i+3j\end{array}$

Step-by-step solution

Step 1. Given information.

$\begin{array}{l}u=4i-0j\\ v=-i+3j\end{array}$

Step 2. Determining the dot product.

The dot product of vectors

$u·v=\left(4\right)(-1)+\left(0\right)\left(3\right)$

$u·v=-4+0$

$u·v=-4$

$u·v\ne 0$

So the vectors u and v are not perpendicular to each other.