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Magnitude of Vector Sum?
When two vectors A and B are drawn from a common point, they form an angle ϕ. Prove that the magnitude of their vector sum is given by √(A^2 + BC^2 + 2ABcosϕ).
Sorry D: I meant B^2
1 Answer
- YohnLv 48 years agoFavorite Answer
You can refer to this figure:
http://www.flickr.com/photos/98361320@N07/92073788...
for angle between vectors, we join head of one vector with the tail of other
I have extended the line of vector A by 'x' , and drawn a perpendicular from the head of vector B onto the extension.
Now we have a big triangle made by vector A, the resultant R (=vector sum), and y,
If we apply pythagoras theorem in it, then R^2 = [(A+x)^2] + [y^2]...........(1)
in the smallest triangle , we have y=Bsinϕ, and x=Bcosϕ,
put these values in that equation (1) to get your answer.
