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
Step 1: Express AD and AE in terms of a and b. Given that D is the midpoint of AB, we have: AD = (1)/(2)AB = (1)/(2)a Given that E is the midpoint of AC, we have: AE = (1)/(2)AC = (1)/(2)b Step 2: Find DE in terms of a and b (part i). To find DE, we can use the vector addition rule: DE = DA + AE Since DA = -AD, we substitute the expressions from Step 1: DE = -(1)/(2)a + (1)/(2)b DE = (1)/(2)(b - a) i) DE = (1)/(2)(b - a) Step 3: Express BC in terms of a and b. To find BC, we can use the vector addition rule: BC = BA + AC Since BA = -AB, we substitute the given vectors: BC = -a + b BC = b - a Step 4: Show that DE = (1)/(2)BC (part ii). From Step 2, we found: DE = (1)/(2)(b - a) From Step 3, we found: BC = b - a Substituting BC into the expression for DE: DE = (1)/(2)BC ii) This shows that DE = (1)/(2)BC.