Vector A has length 4 units and directed to the north. Vector B has length 9 units and is directed to the south. Calculate the magnitude and direction of A+B.
5 units due north
To calculate the magnitude of the vector A+B, we need to find the sum of the magnitudes of vectors A and B.
Magnitude of A = 4 units
Magnitude of B = 9 units
Magnitude of A+B = Magnitude of A + Magnitude of B
Magnitude of A+B = 4 units + 9 units
Magnitude of A+B = 13 units
To determine the direction of A+B, we need to find the resultant angle.
Since vector A is directed to the north and vector B is directed to the south, they are in opposite directions. This means that when we add them, they will cancel each other out.
Thus, the direction of A+B is considered as "zero" or "undefined".
To calculate the magnitude and direction of A+B, we need to find the sum of vector A and vector B.
1. Start by drawing a coordinate system. Place vector A with a length of 4 units directed towards the north (upwards) and vector B with a length of 9 units directed towards the south (downwards).
2. Since vector A is directed to the north and vector B is directed to the south, they have opposite directions. When adding vectors with opposite directions, we subtract their magnitudes.
Subtract the magnitude of vector B (9 units) from the magnitude of vector A (4 units):
4 units - 9 units = -5 units
The magnitude of the sum, A + B, is 5 units. Note that the magnitude is always positive.
3. To determine the direction of A + B, we consider the direction of the resultant vector. In this case, the resultant vector is directed towards the south, which is the direction of vector B.
Thus, the magnitude of A + B is 5 units and it is directed towards the south.
The two vectors are in opposite drections.
If you let positive denote north, the vector sum is 4 - 9 = -5 units.
That means 5 units south.