• Dec 30th 2012, 02:43 PM
princess33407
Evaluate the expression:

v ⋅ w

Given the vectors:

r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>
• Dec 30th 2012, 02:46 PM
jakncoke
Vectors are quite simple.

I'm assume thats $V - W$. Just do component wise subtraction.

For example
$\begin{bmatrix} 5 \\ 6 \end{bmatrix} + \begin{bmatrix} 7 \\ 8 \end{bmatrix} = \begin{bmatrix} 5 + 7 \\ 6 + 8 \end{bmatrix}$

Likewise for subtraction

$\begin{bmatrix} 5 \\ 6 \end{bmatrix} - \begin{bmatrix} 7 \\ 8 \end{bmatrix} = \begin{bmatrix} 5 - 7 \\ 6 - 8 \end{bmatrix}$
• Dec 30th 2012, 02:53 PM
princess33407
I don't understand
• Dec 30th 2012, 03:17 PM
HallsofIvy
Have you ever taken a course involving vectors? If not where did you get this problem? If so, you should have learned that there are a number of operations involving vectors:
1) Addition: <a, b, c>+ <d, e, f>= <a+ d, b+ e, c+ f>.

2) Subtraction: <a, b, c>- <d, e, f>= <a- d, b- e, c- f>.

3) Scalar multiplication: d<a, b, c>= <ad, bd, cd> where d is a "scalar" (number).

4) Dot product or inner product: <a, b, c> . <d, e, f>= ad+ be+ cf. Notice the result is a number, not a vector.

What you wrote is very difficult to read. jakncoke assumed the symbol between the two vectors was a "-" and that you meant to subtract the two vectors:
v- w= <2, -8, -8>- <-2, 6, -5>= <2- (-2), -8- 6, -8- (-5)>= <4, -14, -3>.

It looks to me like "." or dot product: <2, -8, -8>.<-2, 6, -5>= 2(-2)+ (-8)(6)+ (-8)(-5)= -4- 14+ 40= -18+ 40= 22.
• Dec 30th 2012, 03:20 PM
princess33407
So do i use all three of the vectors?
• Dec 30th 2012, 03:25 PM
Plato
Quote:

Originally Posted by princess33407
So do i use all three of the vectors?

There is no way to answer that.
I, for one, have no idea what the question is.

If it is $v\cdot w=~?$ then Halls answered that question in his last line of his reply.
• Dec 30th 2012, 03:25 PM
jakncoke
A vector is basically an arrow pointing the direction and how far youd like to go in that direction. Lets take a 2 dimensional vector, or a vector with 2 components. It basically tells you to go a certain amount of units on the x-axis and then go up a certain amount of units in the y axis

It has the form

$\begin{bmatrix} x \\ y \end{bmatrix}$ where x and y are just numbers like 2,3,4,5.5 etc...

If you want to think visually, this vector tells us to move x units on the X-axis and Y-units in the y axis.

The picture below illustrates graphically what a vector does.
For this example i use the vector $\begin{bmatrix} 2 \\ 2 \end{bmatrix}$

Notice that a vector just tells how where and how far to go from any given point, thats why both the vector (Arrows) colored in black are the same vector $\begin{bmatrix} 2 \\ 2 \end{bmatrix}$

So vector addition, lets take an example, $\begin{bmatrix} 2 \\ 2 \end{bmatrix} + \begin{bmatrix} 3 \\ 4 \end{bmatrix} = \begin{bmatrix} 2 + 3 \\ 2 + 4\end{bmatrix}$ so we have two vectors, one says go 2 units on the x axis and 2 units on the y axis, the second one says go 3 units in the x-axis and 4 units in the y-axis. Adding these two together is like saying, go (2 + 3) or 5 units in the x-axis and then go (2+4) or 6 units in the y-axis.

subtracting vectors is like adding the negative, so $\begin{bmatrix} 2 \\ 2 \end{bmatrix} - \begin{bmatrix} 3 \\ 4 \end{bmatrix} = \begin{bmatrix} 2 \\ 2 \end{bmatrix} + \begin{bmatrix} -3 \\ -4 \end{bmatrix} = \begin{bmatrix} 2-3 \\ 2-4 \end{bmatrix}$ So basically go (2-3) or -1 units on the x-axis and (2-4) or -2 units on the y-axis.
• Dec 30th 2012, 03:29 PM
HallsofIvy
Quote:

Originally Posted by princess33407
So do i use all three of the vectors?

Just because you are taking mathematics there is no reason to throw out common sense!

Suppose the problem had said r= 3, u= 4, v= 5 and asked you to find uv. Would you use all three of the numbers?
• Dec 30th 2012, 03:46 PM
princess33407
Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <10, 6>, v = <9, 5>
• Dec 30th 2012, 03:54 PM
skeeter
Quote:

Originally Posted by princess33407
Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <10, 6>, v = <9, 5>

you should know how to use this formula ...

$\cos{\theta} = \frac{\vec{u} \cdot \vec{v}}{|\vec{u}| |\vec{v}|}$

next time, start a new problem with a new thread, please.
• Dec 30th 2012, 03:57 PM
Plato
Quote:

Originally Posted by jakncoke
A vector is basically an arrow pointing the direction and how far youd like to go in that direction. Lets take a 2 dimensional vector, or a vector with 2 components. It basically tells you to go a certain amount of units on the x-axis and then go up a certain amount of units in the y axis

@jakncoke, I don't normally disagree with this sort of reply. But this time your reply is wrongly over-the-top.

Actually vector really does not have a good mathematical definition.
That is, in mathematics we define terms of set theoretic terms.
BUT we know that a vector is an equivalence class of objects that have the same length & direction .

Now it is possible to define each of those mathematically and then put them together.

So the concept of vectors is so much more than your reply seems to understand.
• Dec 30th 2012, 04:08 PM
jakncoke
Quote:

Originally Posted by Plato
@jakncoke, I don't normally disagree with this sort of reply. But this time your reply is wrongly over-the-top.

Actually vector really does not have a good mathematical definition.
That is, in mathematics we define terms of set theoretic terms.
BUT we know that a vector is an equivalence class of objects that have the same length & direction .

Now it is possible to define each of those mathematically and then put them together.

So the concept of vectors is so much more than your reply seems to understand.

Yes i oversimplified it drastically, but she was having trouble grasping component wise operation, i doubt she would understand much about equivalence classes or set theory. It was just my way of giving her some thread, albeit loose, to hold on to.
• Dec 30th 2012, 04:14 PM
Plato
Quote:

Originally Posted by jakncoke
Yes i oversimplified it drastically, but she was having trouble grasping component wise operation, i doubt she would understand much about equivalence classes or set theory. It was just my way of giving her some thread, albeit loose, to hold on to.

OK
But the actual question is about a dot product.
I think doing anything more is simply confusing.
• Dec 30th 2012, 04:23 PM
jakncoke