This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution to part 7 (b) (i): 7. (b) (i) Find PM Step 1: Identify the given position vectors. The position vector of P from O is OP = p. The position vector of Q from O is OQ = q. Step 2: Find the vector PQ. The vector from P to Q can be expressed as the difference between the position vector of Q and the position vector of P: PQ = OQ - OP PQ = q - p Step 3: Use the information that M is the midpoint of PQ. If M is the midpoint of PQ, then the vector PM is half of the vector PQ. PM = (1)/(2) PQ Step 4: Substitute the expression for PQ into the equation for PM. PM = (1)/(2) (q - p) The vector PM is (1)/(2)(q - p).