Two vectors, A and B, are added by means of vector addition to give a resultant vector R. The magnitudes of A and B are 9 m and 8 m, respectively, and they can have any orientation. What are the maximum and minimum possible values for the magnitude of R?
To find the maximum and minimum possible values for the magnitude of the resultant vector R, we need to consider the different orientations of vectors A and B.
For the maximum magnitude of R, the vectors A and B should be aligned in the same direction. In this case, we can add their magnitudes to get the maximum magnitude of R:
R_max = |A| + |B| = 9 m + 8 m = 17 m
For the minimum magnitude of R, the vectors A and B should be aligned in the opposite direction. In this case, we can subtract their magnitudes to get the minimum magnitude of R:
R_min = |A| - |B| = 9 m - 8 m = 1 m
Therefore, the maximum possible value for the magnitude of R is 17 m, while the minimum possible value is 1 m.
C=a+b
C=9+8
C=17m maximum