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
16. Find the vector PQ Step 1: Identify the coordinates of points P and Q from the diagram. Point P is at (-3, 2). Point Q is at (3, -2). Step 2: Calculate the vector PQ. The vector PQ is found by subtracting the coordinates of P from the coordinates of Q: PQ = Q - P = x_Q - x_P \\ y_Q - y_P PQ = 3 - (-3) \\ -2 - 2 PQ = 3 + 3 \\ -4 PQ = 6 \\ -4 The calculated vector 6 \\ -4 is not among the given options. However, if the question intended to ask for the vector QP (from Q to P), the calculation would be: QP = P - Q = -3 - 3 \\ 2 - (-2) QP = -6 \\ 2 + 2 QP = -6 \\ 4 This matches option C. Assuming there might be a typo in the question and it intended to ask for QP, we select option C. The final answer is C. -6 \\ 4 . 17. Find a + 2b Step 1: Identify the given vectors. a = -2 \\ 3 b = 2 \\ -5 Step 2: Calculate 2b. 2b = 2 2 \\ -5 = 2 × 2 \\ 2 × (-5) = 4 \\ -10 Step 3: Calculate a + 2b. a + 2b = -2 \\ 3 + 4 \\ -10 a + 2b = -2 + 4 \\ 3 + (-10) a + 2b = 2 \\ 3 - 10 a + 2b = 2 \\ -7 This matches option A. The final answer is A. 2 \\ -7 . Send me the next one 📸