How to square a vector..

• Aug 1st 2012, 07:02 AM
mukunku
How to square a vector..
Hello Everyone,

I feel kind of silly asking this but, after numerous tries and ending up with weird results, I needed to make sure. In order to determine if i'm making a mistake in this step, or some other step of my calculations..

Please refer to this image:Attachment 24400

What i can't be sure of is how to square this vector..
Lets say I have three vectors, each with three members:
Code:

```C(1) = {a1,b1,c1} C(2) = {a2,b2,c2} C(3) = {a3,b3,c3}```
So if I wanted to find 'sd' using the equation in the image. Is this how i should calculate my vectors?
Code:

```C(1)2 = {a1*a1 , b1*b1 , c1*c1} C(2)2 = {a2*a2 , b2*b2 , c2*c2} C(3)2 = {a3*a3 , b3*b3 , c3*c3} + __________________________ sd = { SquareRoot[ (a1*a1 + a2*a2 + a3*a3)/N ] , SquareRoot[ (b1*b1 + b2 * b2 + b3 * b3)/N ] , ... }```
I hope I was able to explain myself clearly..

I'd greatly appreciate any help.

Best Regards,
Paul
• Aug 1st 2012, 07:41 AM
HallsofIvy
Re: How to square a vector..
There are three different kinds of "multiplication" defined for vectors: scalar multiplication, the dot product, and, for three dimensional vectors, the cross product.

1) Scalar multipication involves a scalar and a vector so there cannot be a "square".

2) The dot product gives a scalar result: <v1, v2, v3>.<u1, u2, u3>= v1u1+ v2u2+ v3u3 so that the square would be <v1, v2, v3>^2= v1^2+ v2^2+ v3^2 a scalar (number) not a vector.

3) The cross product of two vectors is a vector but it is "anti-commutative" so that the "square", the cross product of a vector with itself is always the 0 vector.

Perhaps a special kind of "vector multiplication" is being defined but your link does not work.
• Aug 1st 2012, 11:40 PM
mukunku
Re: How to square a vector..
@HallsofIvy

I know that vectors have a dot product. But with the equation above, i just couldn't make sense of it.
By "link not working", do you mean the image attachment is not visible?

I'll check my results by getting the dot product again.. And see if I've made any mistakes.
• Aug 2nd 2012, 02:44 AM
mukunku
Re: How to square a vector..
The dot product seems to be producing relatively accurate results.

I guess theres nothing else to be done here =]

Thanks again @HallsofIvy

Note: Can a moderator please change the title prefix to [SOLVED]. I can't seem to edit it [=

Best Regards,
Paul