You are Here: Home >< Maths

# Direction Cosines watch

1. Bit confused here:

It says a_ij is the i component in the E system of ej (e with a line on top).

Does this mean to say that the unit vector in the second co-ordinate system, ej (with a line on top), has components which can be mapped on the first system, which is precisely what a_ij is?
Attached Images

2. (Original post by djpailo)
Bit confused here:

It says a_ij is the i component in the E system of ej (e with a line on top).

Does this mean to say that the unit vector in the second co-ordinate system, ej (with a line on top), has components which can be mapped on the first system, which is precisely what a_ij is?
Yes.

Any vector can be split into compoments.

E and bar{E} (sorry, LaTex is still shot), are two different coordinate systems mapping the same space. Any vector can be described in terms of either coordinate system.

In partiuclar, bar{ej} can be written as a sum of the ei's and is actually sum (i=1 to n) aij ei

The coefficient aij relates to the projection of bar{ej} onto ei, and because they are both unit vectors, this works out to be the cosine of the angle between bar{ej} and ei, that is it's a direction cosine.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 21, 2016
Today on TSR

### The most controversial member on TSR?

Who do you think it is...

### Uni strikes! How do they affect you?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE