Thread: 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

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.

@HallsofIvy
Thanks for the reply!

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?
Try this link: http://i50.tinypic.com/n5oc2g.jpg

I'll check my results by getting the dot product again.. And see if I've made any mistakes.

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