Resultant Vector Homework: Min Value of |A+B+C|

[erisedk]

Homework Statement

Three vectors A, B, C have magnitudes A=5, B=6 and C=7.
The minimum value of |A+B+C| is
*A represents magnitude, A represents the vector (magnitude and direction)

Homework Equations

The Attempt at a Solution

I got 4 because I think that the maximum possible cancellation occurring would be 7-(6+5). But it's wrong.

 

[BiGyElLoWhAt]

Im not sure exactly how to approach this, i have a guess, but ill have to work on it. I am off to bed now, though. An example. Let the magnitude 6 vector point at 120 degrees. Let the 5 magnitude vector point at 60 degrees. Let the 7 vector point directly down. Whats the magnitude? Can you mathematically find a relationship between the vector components and their magnitudes?

 

[erisedk]

I just figured it out, but thanks anyway. The three vectors can form the sides of a triangle, so the minimum will be zero.