Answer to Question #860 in Mechanics | Relativity for duha

Question

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.

Answer 1

We can use this expression for the sum of two vectors:
|A + B |²= |A|² + |B|² - 2 cos(a) |A| |B|
8.4² = 21.0²+21.0² - 2 21.0² cos(a) = 21.0² (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.