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 — Step 1: Express vector r in terms of p and q. Given the equation 2p - 3q + r = 0, we can solve for r: r = -2p + 3q Step 2: Substitute the given vector values for p and q into the expression for r. Given p = 2i - 7j and q = -5i - 9j. r = -2(2i - 7j) + 3(-5i - 9j) Step 3: Perform the scalar multiplication and vector addition. First, multiply the scalars into the vectors: -2(2i - 7j) = -4i + 14j 3(-5i - 9j) = -15i - 27j Now, add these two resulting vectors: r = (-4i + 14j) + (-15i - 27j) Combine the i components and the j components: r = (-4 - 15)i + (14 - 27)j r = -19i - 13j Step 4: Calculate the magnitude of vector r. For a vector r = xi + yj, its magnitude is given by |r| = sqrt(x^2 + y^2). Here, x = -19 and y = -13. |r| = sqrt((-19)^2 + (-13)^2) |r| = sqrt(361 + 169) |r| = sqrt(530) The final answer is sqrt(530). Drop the next question.