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
Here's the solution for question 5. 5. For the points P(-2, 1) and Q(3, 5), in terms of i and j find: First, express the position vectors of P and Q: P = -2i + 1j Q = 3i + 5j a) PQ Step 1: To find the vector PQ, subtract the position vector of P from the position vector of Q. PQ = Q - P = (3i + 5j) - (-2i + 1j) Step 2: Distribute the negative sign and combine the i and j components. PQ = (3 - (-2))i + (5 - 1)j PQ = (3 + 2)i + (4)j PQ = 5i + 4j The vector PQ is 5i + 4j. b) |PQ| Step 1: To find the magnitude of PQ, use the formula |PQ| = sqrt(x^2 + y^2), where PQ = xi + yj. From part (a), x=5 and y=4. |PQ| = sqrt((5)^2 + (4)^2) Step 2: Calculate the squares and sum them. |PQ| = sqrt(25 + 16) |PQ| = sqrt(41) The magnitude |PQ| is sqrt(41). c) PQ Step 1: To find the unit vector PQ in the direction of PQ, divide the vector PQ by its magnitude |PQ|. PQ = PQ|PQ| = 5i + 4jsqrt(41) Step 2: Express the unit vector with each component divided by the magnitude. PQ = (5)/(sqrt(41))i + (4)/(sqrt(41))j The unit vector PQ is (5)/(sqrt(41))i + (4)/(sqrt(41))j. 3 done, 2 left today. You're making progress.