Another i j k vectors question.

[Ricky31290]

Hi everyone. Aftrer doing a search I found loads of information but I still can't 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 I am 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 don't know where to start!

Any help would be much appreciated.
Thanks.

 

[DrClaude]

I understand the basics and how to work out the dot product if given the question in a given way.

In what way do you understand?

 

[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 I am miles out this is all totally new to me!

 

[DrClaude]

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"?

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.

 

[Ricky31290]

Brilliant that's extremely helpful.

Thanks.

 

[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

 

[Mark44]

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

 

[Ricky31290]

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

Sorry, I am a noob!

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