(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?

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# Homework Help: Vector problem in three dimensions

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