Answer
$b=-1$
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 two vectors is $0$, then they are perpendicular or orthogonal. This means that the angle between the two vectors is $90^{\circ}$.
We have the given vectors : $v=i +j$ and $ w=i+bj$
Since, both vectors are orthogonal, then
$v \cdot w=0$
$v \cdot w=(i+j) \cdot (i+bj) =0
\implies (1)(1) +(1)(b) \\=0 \\ \implies 1+b =0 \\ \implies b=-1$
