"Find the coordinates of the point which divides the line segment joining A(2,3,5) to B(3, -1, 1) externally in the ratio 2 : 5. "
How does one solve this problem? And what does "externally" mean?
Hello karldiesenLook at the attached diagram. divides internally in the ratio if ; and divides externally in the ratio if ; or (taking account of the directions) .
Now if points and have position vectors and respectively, then the point that divides the line segment in the ratio has position vector(It's quite straightforward to prove this: begin with , and then say ... etc)
So you can simply plug the position vectors of and into this formula with and . If my arithmetic is correct, I reckon the answer is .
Grandad