(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

First of all, sorry if this isn't the right place to post this.

Four points A, B,C and D have coordinates (0, 1, -2), (1, 3, 2), (4, 3, 4) and (5, -1, -2) respectively. Find the position vectors of

a. The mid-point E of AC

b. The point F on BC such that BF/FD = 1/3

Use your answers to draw a sketch showing the relative positions of A, B, C and D

2. Relevant equations

3. The attempt at a solution

I had no difficulty solving a. and b.: both E and F have position vectors (2i, 2j, k)

This confuses as with respect to the last exercise, though. If E and F have the same position vectors, they should be the same point. Since E lies on AC and F on BC, shouldn’t A, B and C lie on the same line? However, vector AC = 4i + 2j + 6k and vector BC = 3i + 2k: they are not multiples, so A, B and C are not collinear.

I’m new to the study of vectors in three dimensions so there’s probably a noob mistake I’m making somewhere. What am I missing?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector problem in three dimensions

**Physics Forums | Science Articles, Homework Help, Discussion**