Final answer:
The relative position vector for two objects in motion is the difference of their individual position vectors, and the relative velocity vector is obtained by differentiating the relative position vector with respect to time. To visualize these vectors, you draw them based on their components, indicating the movement of one object in relation to the other.
Step-by-step explanation:
To write the position and velocity vector equations for relative motion, we need to consider the motion of one object in relation to another moving object. Let's denote the position vectors of two objects as ℝ₁(t) for object 1 and ℝ₂(t) for object 2. The relative position vector ℝ , which points from object 2 to object 1, is given by ℝ = ℝ₁(t) - ℝ₂(t). The components of ℝ will be the differences in the respective components of ℝ₁ and ℝ₂.
To find the relative velocity vector, we differentiate the relative position vector with respect to time. This gives us ℝ' = ℝ₁'(t) - ℝ₂'(t), where ℝ₁' and ℝ₂' are the velocity vectors of object 1 and object 2, respectively.
To draw the position and velocity vectors for relative motion, one must plot the vectors ℝ₁ and ℝ₂ from a common origin, and then draw vector ℝ originating from the tip of ℝ₂ and terminating at the tip of ℝ₁. The relative velocity vector ℝ' is then drawn tangentially to the path of ℝ, representing the direction and rate at which object 1 is moving away from or towards object 2.