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?
What would be R if A,B are in the same direction? In the opposite directions?
SAME: 9+8=17 (max)
OPPOSITE: 9-8=1 (min)
Is that right?
To find the maximum and minimum possible values for the magnitude of R, we need to consider the different orientations of vectors A and B.
First, let's consider the case where vector A and vector B are pointing in the same direction. In this case, the magnitude of R will be the addition of the magnitudes of A and B:
R = A + B = 9 m + 8 m = 17 m
Therefore, the maximum possible value for the magnitude of R is 17 m.
Next, let's consider the case where vector A and vector B are pointing in opposite directions. In this case, the magnitude of R will be the subtraction of the magnitudes of A and B:
R = A - B = 9 m - 8 m = 1 m
Therefore, the minimum possible value for the magnitude of R is 1 m.
In summary, the maximum possible value for the magnitude of R is 17 m, and the minimum possible value is 1 m.