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
Given the vectors m = 1i + 2j and n = 3j. i) The angle between m and n Step 1: Calculate the dot product of m and n. The vectors can be written as m = 1 \\ 2 and n = 0 \\ 3 . m · n = (1)(0) + (2)(3) = 0 + 6 = 6 Step 2: Calculate the magnitudes of m and n. |m| = sqrt(1^2 + 2^2) = sqrt(1 + 4) = sqrt(5) |n| = sqrt(0^2 + 3^2) = sqrt(9) = 3 Step 3: Use the dot product formula to find the angle . The formula is = m · n|m| |n|. = (6)/(sqrt(5) · 3) = (2)/(sqrt(5)) = ((2)/(sqrt(5))) ≈ 26.57^ The angle between m and n is 26.57^. ii) The projection of m on n Step 4: Calculate the scalar projection of m on n. The scalar projection of vector A on vector B is given by comp_B A = A · B|B|. Using the values from previous steps: comp_n m = m · n|n| = (6)/(3) = 2 The projection of m on n is 2. Send me the next one 📸