Okay, let's say the vectors have the following components:

This tells us thatThree vectors x, y, and z satisfy x + y + z = 0.

Using the dot product property we have|x| = 2, |y| = 3, and |z| = 4

In terms of the components, what we are trying to find isCalculate the value of

Rearranging and substituting from the above, we have