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
Hey Adeyemi, good to see you again. To show that two vectors are parallel, we need to demonstrate that one vector is a scalar multiple of the other. That is, if a and b are two vectors, they are parallel if a = cb for some scalar c. Step 1: Define the given vectors. Let v_1 = 4i - 6j + 9k Let v_2 = -6i + 9j - (27)/(2)k Step 2: Assume v_2 = cv_1 and find the scalar c. We set the components equal to each other: -6i + 9j - (27)/(2)k = c(4i - 6j + 9k) -6i + 9j - (27)/(2)k = 4ci - 6cj + 9ck Step 3: Equate the coefficients for each component. For the i component: -6 = 4c c = (-6)/(4) = -(3)/(2) For the j component: 9 = -6c c = (9)/(-6) = -(3)/(2) For the k component: -(27)/(2) = 9c c = (-27/2)/(9) = (-27)/(2 × 9) = (-27)/(18) = -(3)/(2) Step 4: Conclude based on the scalar value. Since the scalar c = -(3)/(2) is consistent for all components, the vectors are parallel. Therefore, v_2 = -(3)/(2)v_1. The vectors 4i - 6j + 9k and -6i + 9j - (27)/(2)k are indeed parallel. The vectors are parallel because v_2 = -(3)/(2)v_1 Send me the next one 📸