Triangle law of vector addition vs Pythagorean theorem Suppose there is a vector a of magnitude 5 units to the east, another vector b of magnitude 6 units to the north. To find magnitude of vector a + vector b, 
By the triangle law of vector addition, it is 5 + 6 units = 11 units.
By Pythagorean theorem, it is sqrt(5^2 + 6^2) = sqrt(61)
Which answer is right? If so, why is the other wrong? 
Thank you!
 A: The Pythagorean theorem answer is the right one. The problem with the other is that it's based on a misunderstanding of the triangle law of vector addition.
The triangle law of vector addition shows you how to add two vectors to get another vector. Its purpose is just to convey that vector addition corresponds to the triangle picture. What you appear to have extrapolated is that this corresponds to adding magnitudes (lengths) of vectors, too. Adding vectors is different from adding lengths. In the language of vectors, the correct answer to your question is the magnitude of the sum of your two vectors. As another poster noted, your two vectors are [5,0] and [0,6], which sum to [5,6]. You are interested in the magnitude of the vector [5,6], which is given by the Pythagorean formula $\sqrt{5^2 + 6^2}$, not $5+6$.
A: Adding vectors means more than just adding their magnitudes. In your case, the vector 5 units to the east can be represented as $[5,0]$, while the vector to the north is $[0,6]$. Adding these gives $[5,0]+[0,6]=[5,6]$. What is the magnitude of $[5,6]$?
