Vectors

Step 1: Understanding the Concept:
For collision: relative velocity must be along the line joining the two particles, i.e., along relative displacement.
Step 2: Detailed Explanation:
At time : . Rearranging: . So displacement vector must be parallel to relative velocity . This gives the unit vector condition (option A).
Step 3: Final Answer:

Step 1: Understanding the Concept:
For three forces to be in equilibrium, they must form a closed triangle when represented as vectors.
Step 2: Detailed Explanation:
For three forces of equal magnitude to be in equilibrium, they must be at to each other. When these forces are represented as sides of a triangle, they form an equilateral triangle.
Step 3: Final Answer:
The angle is and the triangle is equilateral.