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
Alright Hurry — let's do this. To calculate the angle PSQ, we need to find the vectors SP and SQ and then use the dot product formula. Given position vectors: P = -2i + 3j Q = 3i + 4j S = 3i Step 1: Find the vector SP. SP = P - S SP = (-2i + 3j) - (3i) SP = (-2 - 3)i + (3 - 0)j SP = -5i + 3j Step 2: Find the vector SQ. SQ = Q - S SQ = (3i + 4j) - (3i) SQ = (3 - 3)i + (4 - 0)j SQ = 0i + 4j = 4j Step 3: Calculate the dot product SP · SQ. SP · SQ = (-5)(0) + (3)(4) SP · SQ = 0 + 12 = 12 Step 4: Calculate the magnitudes of SP and SQ. |SP| = sqrt((-5)^2 + (3)^2) = sqrt(25 + 9) = sqrt(34) |SQ| = sqrt((0)^2 + (4)^2) = sqrt(0 + 16) = sqrt(16) = 4 Step 5: Use the dot product formula = a · b|a| |b| to find PSQ. ( PSQ) = SP · SQ|SP| |SQ| ( PSQ) = (12)/(sqrt(34) × 4) ( PSQ) = (12)/(4sqrt(34)) ( PSQ) = (3)/(sqrt(34)) Step 6: Calculate the angle to the nearest degree. PSQ = ((3)/(sqrt(34))) PSQ ≈ (0.51450) PSQ ≈ 59.04^ Rounding to the nearest degree, the angle is 59^. The angle PSQ is 59^. Send me the next one 📸