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
let's explain question (3) again. 3) Given PQ = 2 \\ 3 and OQ = -1 \\ 4 . Find the coordinates of P. Step 1: Understand the relationship between position vectors and displacement vectors. A displacement vector from point P to point Q, denoted as PQ, can be found by subtracting the position vector of the starting point P (OP) from the position vector of the ending point Q (OQ). So, the fundamental relationship is: PQ = OQ - OP Our goal is to find the coordinates of P, which are represented by the position vector OP. We need to rearrange the equation to solve for OP. Add OP to both sides and subtract PQ from both sides: OP = OQ - PQ Step 2: Substitute the given vectors into the rearranged equation. We are given OQ = -1 \\ 4 and PQ = 2 \\ 3 . OP = -1 \\ 4 - 2 \\ 3 Step 3: Perform the vector subtraction. To subtract vectors, you subtract their corresponding components (x-component from x-component, y-component from y-component). OP = -1 - 2 \\ 4 - 3 Step 4: Calculate the resulting components. OP = -3 \\ 1 Step 5: State the coordinates of P. The position vector OP = -3 \\ 1 means that point P has coordinates (-3, 1). The coordinates of P are (-3, 1). What's next?