Imagine you are at a point A, a café you visit often. Your friend is at the point B, a bookstore a…

Imagine you are at a point A, a café you visit often. Your friend is at the point B, a bookstore a few blocks away on a straight road. You want to meet your friend at a point on the line joining the café and the bookstore. Another friend, who is at home on the other side of the same road represented by point P, also wants to join. You decide to determine the exact meeting point by finding the foot of the perpendicular from P on the line joining the café and the bookstore. Given that co-ordinates of the café (A) are $(1, 2, 4)$, of the bookstore (B) are $(3, 4, 5)$ and the home are $(2, 1, 3)$, find the location of the meeting point.