Final Answer:
The position vector, r, from point A to point B is r = 19 m i + 12 m j - 16 m k.
Step-by-step explanation:
To determine the position vector, r, from point A to point B, we subtract the coordinates of point A from the coordinates of point B. The position vector is represented as r = (x2 - x1) i + (y2 - y1) j + (z2 - z1) k, where i, j, and k are the unit vectors in the x, y, and z directions respectively. Using the given coordinates, we calculate the differences in each direction: x2 - x1 = 19 m - 12 m = 7 m, y2 - y1 = 12 m - 16 m = -4 m, and z2 - z1 = 16 m - (-20 m) = 36 m. Therefore, the position vector, r, from point A to point B is r = 7 m i - 4 m j + 36 m k.
This position vector represents the displacement from point A to point B in a three-dimensional space. The components of the vector indicate the change in position along each axis. The unit vectors, i, j, and k, represent the directions of the x, y, and z axes respectively. By calculating the differences in coordinates and expressing them as a vector, we can precisely describe the displacement between the two points in a clear and concise manner.
Understanding position vectors is crucial in physics, engineering, and various other fields where spatial relationships and displacements are analyzed. These vectors provide a mathematical representation of positions and displacements in multiple dimensions, allowing for accurate calculations and predictions in diverse applications.