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 6: Step 1: Substitute the given column vectors into the expression for a. The expression for a is a = 2p - (3)/(4)q + (2)/(3)r. a = 2 -3 \\ 4 - (3)/(4) 16 \\ -4 + (2)/(3) 9 \\ 6 Step 2: Perform the scalar multiplication for each term. 2 -3 \\ 4 = 2 × -3 \\ 2 × 4 = -6 \\ 8 (3)/(4) 16 \\ -4 = (3)/(4) × 16 \\ (3)/(4) × -4 = 12 \\ -3 (2)/(3) 9 \\ 6 = (2)/(3) × 9 \\ (2)/(3) × 6 = 6 \\ 4 Step 3: Substitute the results back into the expression for a and perform vector addition/subtraction. a = -6 \\ 8 - 12 \\ -3 + 6 \\ 4 a = -6 - 12 + 6 \\ 8 - (-3) + 4 a = -12 \\ 15 Step 4: Calculate the magnitude of vector a. The magnitude of a vector x \\ y is given by sqrt(x^2 + y^2). |a| = sqrt((-12)^2 + (15)^2) |a| = sqrt(144 + 225) |a| = sqrt(369) Step 5: Simplify the square root. |a| = sqrt(9 × 41) |a| = 3sqrt(41) The column vector a is -12 \\ 15 Its magnitude is 3sqrt(41) What's next?