Question

Two particles moving with constant velocity are described by the position vectors: .p = p₀ + vt, s= S₀ + wt. Find the shortest distance between the particles themselves.

Answer 1

The shortest distance between the particles themselves can be found by calculating the displacement vector, which is the difference between their position vectors.

Step-by-step explanation:

The shortest distance between the particles themselves can be found by calculating the displacement vector, which is the difference between their position vectors. Let's calculate it step by step:

1. Subtract the initial position vectors p₀ and S₀ to find the displacement vector: d = p₀ - S₀
2. Use the property of vector addition where the scalar multiples can be factored out: d = p₀ - S₀ = p₀ + (-S₀)
3. Use the distributive property to distribute the scalar -1 to the vector S₀: d = p₀ + (-S₀) = p₀ + (-1)S₀
4. Add the displacement vectors p₀ and (-1)S₀ to find the shortest distance between the particles: d = p₀ + (-1)S₀ = p₀ - S₀

The shortest distance between the particles themselves is given by the displacement vector d = p₀ - S₀.