Answer
$[(x-x_0) i+(y-y_0) j] \cdot (Ai+Bj) =A(x-x_0) +B(y-y_0)=0$;
Thus, we have verified the given formula.
Work Step by Step
The equation for a line vector can be expressed as:
$v=(x-x_0) i+(y-y_0) j$
Next, the line is passing through the points $(x_0,y_0)$ and $(x,y)$ .
So, the vector $n = Ai+Bj$ is normal to it.
$\implies v \cdot n =0$
$\implies [(x-x_0) i+(y-y_0) j] \cdot (Ai+Bj) =A(x-x_0) +B(y-y_0)=0$
Verified.
