Vector Calculation: Finding Magnitude with Given Vectors

[Fineline]

Three vectors x, y and z satisfy x + y + z = 0. Calculate the value of
(x dot y) + (x dot z) + (y dot z) if the magnitude of x is 2, the magnitude of y is 3, and the magnitude of z is 4.

Sorry I don't have time to format this properly, I've got to run off to work. This question has been bugging me, and any help would be greatly appreciated.

 

[arildno]

Dot your equation with x, y and z, and add the results and see something fun happening.

 

[Fineline]

Sorry, but I'm not sure I follow.

 

[tiny-tim]

Do a bit at a time!

Hi Fineline! Welcome to PF!

(btw, it's ok to write x.y + x.z + y.z, once you've made it clear that x y and z are vectors.)

Yes, I don't follow either: x.y etc is a scalar, so you can't dot it with anything.

Hint: Can you calculate x.y + x.z? And then …

 

[Tedjn]

I do not have any experience with these problems, so I don't know the standard way to approach it. One possible approach, however, is to find what (x + y + z)² is when expanded.

 

[tiny-tim]

One possible approach, however, is to find what (x + y + z)² is when expanded.

ooo! Your method is even nicer than mine!

 

[Hurkyl]

Sorry, but I'm not sure I follow.

You have an arithmetic operation. (dot product) Use it. In as many ways as you can imagine.

 

[Fineline]

Alright, thanks everyone, I got it all worked out.