Evaluate the expression:
v ⋅ w
Given the vectors:
r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>
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.
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
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
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
So vector addition, lets take an example, 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 So basically go (2-3) or -1 units on the x-axis and (2-4) or -2 units on 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.