Which is the vector quantity that describes the shortest path between two points?
if the vectors for the points p and q are u and v, then u-v points straight from q to p.
The vector quantity that describes the shortest path between two points is called the displacement vector. It is denoted by a symbol such as "d" or "Δr" and represents the change in position from the initial point to the final point. To calculate the displacement vector, you will need the position vectors of the initial and final points.
To find the displacement vector, follow these steps:
1. Identify the initial point (let's call it A) and the final point (let's call it B).
2. Express the position vectors of point A and B as vectors. Let's say the position vector of point A is represented by vector A, and the position vector of point B is represented by vector B.
3. Subtract vector A from vector B. This can be done by subtracting the corresponding components of the two vectors. For example, if vector A has components (Ax, Ay, Az) and vector B has components (Bx, By, Bz), then you find the displacement vector by calculating (Bx - Ax, By - Ay, Bz - Az).
4. The resulting vector is the displacement vector. It represents the shortest path between points A and B, taking into account both the magnitude (the distance between the points) and the direction (the straight line connecting the points).
Remember that the displacement vector is a vector quantity, meaning it has magnitude and direction. The magnitude of the displacement vector represents the shortest distance between the two points, while the direction of the displacement vector represents the straight line connecting the two points.