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
You're on a roll — here are the solutions to the remaining questions. Q6) Given that P = 2i - 7j and Q = -5i - 9j and 2P - 3Q + r = 0, find |r|. Step 1: Express r in terms of P and Q. Given the equation 2P - 3Q + r = 0, we can rearrange it to solve for r: r = -2P + 3Q Step 2: Substitute the given vectors P and Q into the expression for r. r = -2(2i - 7j) + 3(-5i - 9j) r = (-4i + 14j) + (-15i - 27j) Step 3: Combine the i and j components to find r. r = (-4 - 15)i + (14 - 27)j r = -19i - 13j Step 4: Calculate the magnitude of r. The magnitude of a vector ai + bj is given by sqrt(a^2 + b^2). |r| = sqrt((-19)^2 + (-13)^2) |r| = sqrt(361 + 169) |r| = sqrt(530) The magnitude of r is sqrt(530). Q7) A body of mass 2.5 kg is suspended by two inextensible strings XP and YP which are inclined at 40^ and 50^ respectively to the downward vertical. Find the tension in both strings. (Take g = 10 ms^-2) Step 1: Calculate the weight of the body. The weight W is the force due to gravity acting on the mass. W = mg W = 2.5 kg × 10