# Another i j k vectors question.

1. Oct 29, 2015

### Ricky31290

Hi everyone. Aftrer doing a search I found loads of information but I still cant get my head around these damm vectors. I understand the basics and how to work out the dot product if given the question in a given way.

An example of the questions im being asked are:

The following two vectors are:
p = 4i + 3j - 2k and q = 2i - 4j - 3k
i) Find p+ q
ii) Find p – q
iii) Find the scalar product of pq
iv) Find the direction cosines for both p and q
v) Find the angle between vectors p and q, giving your answer to 2 decimal places (d.p.)

When the vectors are written in this form I literally dont know where to start!

Any help would be much appreciated.
Thanks.

2. Oct 29, 2015

### Staff: Mentor

In what way do you understand?

3. Oct 29, 2015

### Ricky31290

By using the (a)(b)cos0 rule.

To use this I would need to know what a b and the angle would be. So if its drawn for me (almost like a tri angle) its straight forward. I take it the "i j k" must refer to "a b 0"?

Sorry if im miles out this is all totally new to me!

4. Oct 29, 2015

### Staff: Mentor

No. i, j, and k are unit vectors (vectors of length 1), pointing along the x, y, and z axes, respectively. Take p, for instance. You have
$$\mathbf{p} = 4 \mathbf{i} + 3 \mathbf{j} - 2 \mathbf{k} = 4 \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} + 3 \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} -2 \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 4 \\ 3 \\ -2 \end{pmatrix}$$
which represents a vector with its origin at $(x,y,z) = (0,0,0)$ and its tip at $(4,3,-2)$.

You will need to get your hands on a good book on linear algebra. I don't know much about web resources, but there is a very basic introduction on Math is Fun. You can also have a look at Khan Academy.

5. Oct 29, 2015

### Ricky31290

Thanks.

6. Oct 29, 2015

### HallsofIvy

(a, b, c)+ (p, q, r)= (a+ p, b+ q, c+ r).

And the scalar product is (a, b, c).(p, q, r)= ap+ bq+ cr

7. Oct 29, 2015

### Staff: Mentor

Thread moved out of homework sections, as this question is not specifically a homework question.

8. Oct 30, 2015

### Ricky31290

Sorry, im a noob!

For anybody else looking for help on this subject I found this website very helpful.. http://www.mathtutor.ac.uk/