Let rA and rB be the position vectors of points A and B resp

Let rA and rB be the position vectors of points A and B, respectively and consider all points r = (rA + rB )/( + ) for all real and with +=0. Do these points lie along a line or a plane?

Solution

They will lie along a line because r = (rA + rB )/( + ) this formula is just the section formula for two points where r divides two points in the ratio : .