Understanding Vector Addition and Magnitude Equality

[yoyo16]

Homework Statement

If vector A + vector B = vector C and magnitude A + magnitude B = magnitude C how are vector A and B relative to each other.

Homework Equations

The Attempt at a Solution

I need help understanding this question. I know that in order for them to be equal they must be in the same direction. Also, does this mean that the vectors form a right angle to teach other in order for he magnitudes to be equal. Please help me, I'm so confused.

 

[grzz]

Try to draw a diagram which shows that mag A + mag B = mag C.

 

[jackarms]

Yes, you're right that since the magnitudes of A and B add up to C, then all three vectors must be in the same direction. Not quite sure what you mean by the vectors forming a right angle -- they'll just all be in the same direction. Knowing that, how would A and B line up to form C?

 

[yoyo16]

But what would be the relationship between the two vectors? How can I prove that they are equal?

 

[jackarms]

But you don't know that A and B are equal -- only that they add up to C. I think the question just asks how A and B are oriented relative to each other.

 

[yoyo16]

So when drawing out the vector and magnitude diagrams, they both would look exactly alike?

 

[jackarms]

But that would mean that A and B are equal in magnitude, which you don't know. Did you draw out the diagram? If you just draw A and B to have arbitrary lengths (so long as they add up to C), what else can you say about A and B in terms of orientation?

 

[yoyo16]

Im not sure. It comes out to be a triangle?

 

[jackarms]

Usually that's what vector addition looks like, but is that the case for here? If A and B are sides of a triangle, and if C is the the other, longest side, then what happens when A and B add up to C?

 

[yoyo16]

a^2+b^2=c^2

 

[jackarms]

If you could do some more explaining with words, that would help out -- that formula isn't really relevant here. Just talk about what you think will happen if two sides of a triangle add up to the third side. Try to draw a picture of it.

 

[yoyo16]

I think that A and B would add up to make the resultant vector C. That means A and B would be perpendicular to each other.

 

[jackarms]

Not necessarily though. In that case A, B, and C would form a right triangle, but you also have to have |A| + |B| = |C| (|A| means magnitude of A), in which case a right triangle wouldn't work, since you can't add the legs of a right triangle to get the hypotenuse.