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
Fresh day Jedidah🎀, let's solve. Given: • OA = 2p • OQ = q • Q is the midpoint of OC, so OC = 2OQ = 2q. • OABP is a straight line. • From the diagram, OA = AB = BP. Since OA = 2p, it follows that AB = 2p and BP = 2p. a) Express OB in terms of p and/or q. Step 1: Use the vector addition rule OB = OA + AB. OB = 2p + 2p OB = 4p The final answer is 4p. b) Express BC in terms of p and/or q. Step 1: Use the vector addition rule BC = BO + OC. We know BO = -OB = -4p and OC = 2q. BC = -4p + 2q The final answer is -4p + 2q. c) Express AQ in terms of p and/or q. Step 1: Use the vector addition rule AQ = AO + OQ. We know AO = -OA = -2p and OQ = q. AQ = -2p + q The final answer is -2p + q. d) Express CP in terms of p and/or q. Step 1: Use the vector addition rule CP = CO + OP. We know CO = -OC = -2q. Step 2: Calculate OP. OP = OA + AB + BP OP = 2p + 2p + 2p OP = 6p Step 3: Substitute CO and OP into the expression for CP. CP = -2q + 6p The final answer is 6p - 2q. What's next?