# Algebraic vectors

1. Jun 4, 2006

### masterofthewave124

if i had to find a vector of magnitude 27 units which is parallel to 3i+ 4j, what do i have to do first? would i express my answer in ordered pair notation?

2. Jun 4, 2006

### Hootenanny

Staff Emeritus
I would express your answer in terms of unit vectors. Ordered pair notation is uaually used to define co-ordinates. Remember parallel vectors must be multipuls of each other.

~H

3. Jun 4, 2006

### masterofthewave124

would this be a sufficient answer:

let u be the vector.

the magnitude of 3i + 4j is 5

27/5 = 5.4

since parallel vectors are multiples of each other, we can just multiply (3i + 4j) by the scalar 5.4

so u = 5.4(3i + 4j)
= 16.2i + 21.6j

this is what i came up with before but it seems messy (decimals) and and kind of an inefficient solution

4. Jun 4, 2006

### arildno

$$u=\frac{27}{5}(3i+4j)$$

Note that $\frac{1}{5}(3i+4j)$ is a UNIT vector.

5. Jun 4, 2006

### masterofthewave124

looks much better. thanks!

6. Jun 4, 2006

### Hootenanny

Staff Emeritus
Who said it wasn't a unit vector?

7. Jun 4, 2006

### arildno

Noone. I just wanted to emphasize that, so that OP could see how a unit vector naturally would occur in his expression.

8. Jun 4, 2006

### Hootenanny

Staff Emeritus
Ahh right, I thought I'd made a mistake somewhere .

9. Jun 4, 2006

### arildno

No, but I wanted OP to see why your suggestion
is, indeed, the most natural one.

10. Jun 4, 2006

### Hootenanny

Staff Emeritus
Good point, I should have emphisised (but I didn't get the chance )

11. Jun 4, 2006

### masterofthewave124

guys, i have some more questions if you don't mind.

state whether the following expressions are vectors, scalars or meaningless:
a) (a+b) • (a+c)
b) (a • a)b
c) (a • b)• c(b × c)

note that all the letters are vectors (so picture arrows on top of them)

mostly i need to clairify some things. first, whats the difference between a scalar and something meaningless? also for b) and c), what does something like (a • a)b compute to. does the b multiply, or dot, or cross or what?

12. Jun 4, 2006

### arildno

Something "meaningless" is an indicated operation between quantities that the operation in question cannot, by definition, be used upon.

13. Jun 4, 2006

### masterofthewave124

oh ok, so since the dot and cross products are only applicable to vectors, if a scalar was involved in one of them, the result would be meaningless?

to restate my other question, what does the b part of (a • a)b compute to. does the b multiply, or dot, or cross or what?

14. Jun 4, 2006

### arildno

Remember that you have 3 basic product operations with vectors:
1. Dot product: Takes two vectors and produces a scalar.
2. Cross product: Takes two vectors and produces a vector.
3. Scalar multiplication: Takes a scalar and a vector, produces a vector that is parallell to the original vector.

15. Jun 4, 2006

### masterofthewave124

thanks for the summary but the way (a • a)b is written, and considering b is a vector and not a scalar, what is the operation here?

16. Jun 4, 2006

### arildno

What does a parenthesis usually signify for the order of operations performed?

17. Jun 4, 2006

### masterofthewave124

so i think your referring to doing the inside of the brackets first; a dot product operation yielding a scalar. so then does it leave a scalar multiplying a vector?

18. Jun 4, 2006

### arildno

What do YOU think?

19. Jun 4, 2006

### masterofthewave124

lol that's what i think, i do have some doubt however because as you look at c) (a • b) • c(b × c), the second part of the question (c(b × c)) is somewhat confusing. you basically get a vector multiplying a vector without dot or cross product operation (the only two ways you can muliply vectors i'm aware of). although this does not change the outcome of the question since the first part of the question is a scalar and yielding the result meaningless.

20. Jun 4, 2006

### arildno

Correct!
Either way you are looking upon the last one, either as:
$$((a\cdot{b})\cdot{c})(b\times{c})$$
or as:
$$(a\cdot{b})\cdot({c}(b\times{c}))$$
the expressions are meaningless.