Answer to Question #860 in Mechanics | Relativity for duha
Question #860
Vectors and have equal magnitudes of 21.0. If the sum of and is the vector 8.40 , determine the angle between A and B.
Expert's answer
We can use this expression for the sum of two vectors:
|A + B |^{2}= |A|^{2} + |B|^{2} - 2 cos(a) |A| |B|
8.4^{2} = 21.0^{2}+21.0^{2} - 2 21.0^{2} cos(a) = 21.0^{2} (2(1-cos(a))
70.56 = 882 (1-cos(a))
1-cos(a) = 0.08
cos(a) = 0.92
a = 23 deg
The angle between A and B equals to 23 degrees.
|A + B |^{2}= |A|^{2} + |B|^{2} - 2 cos(a) |A| |B|
8.4^{2} = 21.0^{2}+21.0^{2} - 2 21.0^{2} cos(a) = 21.0^{2} (2(1-cos(a))
70.56 = 882 (1-cos(a))
1-cos(a) = 0.08
cos(a) = 0.92
a = 23 deg
The angle between A and B equals to 23 degrees.
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