"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?
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 .