The magnitudes of two vectors vector A and vector B are 20 units and 5 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector vector R = vector A + vector B ?
largest:? units
Smallest:? units
The largest value of A+B is when they act in the same direction, and the resultant is the sum of the magnitudes.
The smallest value of A+B is when they act in opposite directions, and the resultant is the difference of the magnitudes.
25 largest and 15 for smallest
Well, the largest possible value for the magnitude of the resultant vector R is when vector A and vector B are pointing in the same direction. In this case, we simply add the magnitudes of the two vectors to get the largest value:
largest = 20 units + 5 units = 25 units
On the other hand, the smallest possible value for the magnitude of the resultant vector R is when vector A and vector B are pointing in completely opposite directions and cancel each other out. In this case, we subtract the smaller magnitude from the larger magnitude to get the smallest value:
smallest = 20 units - 5 units = 15 units
So, the largest possible value for the magnitude of the resultant vector R is 25 units, and the smallest possible value is 15 units.
To find the largest and smallest possible values for the magnitude of the resultant vector R = A + B, we need to consider the scenarios where the two vectors are aligned in the same direction and in opposite directions.
1. Aligned in the same direction:
In this case, the magnitude of the resultant vector R will be the sum of the magnitudes of vectors A and B because they are contributing in the same direction. So, the largest possible value for R will be when both vectors are aligned in the same direction:
R_max = |A| + |B| = 20 + 5 = 25 units
2. Aligned in opposite directions:
In this case, the magnitude of the resultant vector R will be the difference between the magnitudes of vectors A and B because one vector partially cancels out the other due to their opposite directions. So, the smallest possible value for R will be when both vectors are aligned in opposite directions:
R_min = |A| - |B| = 20 - 5 = 15 units
Therefore, the largest possible value for the magnitude of the resultant vector R is 25 units, and the smallest possible value is 15 units.