Answer
$a=\dfrac{2}{3}$
Work Step by Step
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$.
The dot product is given as: $v \cdot w=(pi+qj) \cdot (xi+yj) =px+qy$
We know that when the dot product between the two vectors is $0$, then they are perpendicular or orthogonal. This means that the angle between the two vectors is $90^{\circ}$.
In our case, we have the vectors:
$v=i-aj$ and $ w=2i+3j$
Since, both vectors are orthogonal, then
$v \cdot w=0$
$v \cdot w=(i-aj) \cdot (2i+3j) =0
\implies (1)(2) +(-a)(3) \\=0 \\ \implies 2-3a =0 \\ \implies a=\dfrac{2}{3}$
