Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_1

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/1 Determine the angles made by the vector with the positive - and - axes. Write the unit vector in the direction of . Problem 1/1 (a) Angles with the positive - and -axes ● Calculation Process 1. Magnitude of the vector: First, we must calculate the magnitude of the given vector . 2. Substitute Values for Magnitude: With and : 3. Determine direction angles: The angles and that a vector makes with the positive axes are defined by its direction cosines: 4. Final Calculation for Angles: For the -axis: For the -axis: ● Final Conclusion: The vector makes an angle of with the positive -axis and with the positive -axis. (b) Unit vector in the direction of ● Calculation Process V=40i−30jxy nV xy V V=V i+ x V j y V=∣V∣= V +V x 2 y 2 V = x 40V = y −30 V= (40)+(−30) 22 V= = 1600+900 = 250050 θ x θ y cosθ = x ,cos θ = V V x y V V y xcosθ = x = 50 40 0.8⟹θ = x cos(0.8)≈ −1 36.87 ∘ ycosθ = y = 50 −30 −0.6⟹θ = y cos(−0.6)≈ −1 126.87 ∘ 36.9 ∘ x 126.9 ∘ y nV 1. Present Final Formula: The unit vector in the direction of is obtained by dividing the vector by its magnitude. 2. Substitute Values: 3. Final Calculation: ● Final Conclusion: The unit vector is . ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 1/1 nV n= = V V i+ V V x j V V y n= 50 40i−30j n= i− 50 40 j 50 30 n=0.8i−0.6j n=0.8i−0.6j θ = x 36.9,θ = ∘ y 126.9 ∘ n=0.8i−0.6j