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
2. Find the sum of the vectors 3i + 7j and 2i - 2j. Step 1: Add the corresponding i components and j components of the two vectors. (3i + 7j) + (2i - 2j) = (3+2)i + (7-2)j Step 2: Simplify the expression. (3+2)i + (7-2)j = 5i + 5j The sum of the vectors is 5i + 5j 3. If the position vectors of P and Q are i + 3j and 5i - 2j respectively, find PQ and |PQ|. Step 1: Find the vector PQ by subtracting the position vector of P from the position vector of Q. Let P = i + 3j and Q = 5i - 2j. PQ = Q - P = (5i - 2j) - (i + 3j) Step 2: Distribute the negative sign and combine like terms. PQ = (5-1)i + (-2-3)j = 4i - 5j Step 3: Find the magnitude of PQ, denoted as |PQ|. If PQ = xi + yj, then |PQ| = sqrt(x^2 + y^2). Here, x=4 and y=-5. |PQ| = sqrt((4)^2 + (-5)^2) Step 4: Calculate the squares and sum them. |PQ| = sqrt(16 + 25) = sqrt(41) The vector PQ is 4i - 5j and its magnitude |PQ| is sqrt(41). Send me the next one 📸