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 the given vectors in component form. Given OP = i - 3j, so the position vector of P is 1 \\ -3 . Given PQ = 4i - 2j, so the vector from P to Q is 4 \\ -2 . a) The coordinates of Q. To find the position vector of Q, we add the vector OP and the vector PQ. OQ = OP + PQ OQ = 1 \\ -3 + 4 \\ -2 OQ = 1+4 \\ -3-2 OQ = 5 \\ -5 The coordinates of Q are (5, -5). b) |PQ| in surd form. The vector PQ = 4i - 2j. The magnitude of a vector v = ai + bj is given by |v| = sqrt(a^2 + b^2). For PQ = 4i - 2j, we have a=4 and b=-2. |PQ| = sqrt(4^2 + (-2)^2) |PQ| = sqrt(16 + 4) |PQ| = sqrt(20) To express this in surd form, we simplify sqrt(20): sqrt(20) = sqrt(4 × 5) sqrt(20) = sqrt(4) × sqrt(5) |PQ| = 2sqrt(5) The final answers are: a) The coordinates of Q are (5, -5). b) |PQ| in surd form is 2sqrt(5). Send me the next one 📸