Solutions of Engineering Electromagnetics with Questions and Answers

Solutions of Engineering Electromagnetics with Questions and Answers A vector A has magnitude 10 and makes angles α = 60°, β = 45°, γ = 60° with x, y, z axes respectively. Which of the following represents its correct Cartesian form? a) 5i + 7.07j + 5k b) 8.66i + 7.07j + 8.66k c) 5i + 5j + 5k d) 7.07i + 5j + 8.66k Correct Answer: a Rationale: The Cartesian components are A_x = A cos α = 10 cos 60° = 5, A_y = 10 cos 45° ≈ 7.07, A_z = 10 cos 60° = 5, giving 5i + 7.07j + 5k. A vector B = 3i − 4j + 12k. What is its unit vector? a) (3/13)i − (4/13)j + (12/13)k b) (3/11)i − (4/11)j + (12/11)k c) (1/13)(3i − 4j + 12k) d) (3/169)i − (4/169)j + (12/169)k Correct Answer: a Rationale: Magnitude of B is √(9 + 16 + 144) = √169 = 13, so unit vector is B/|B| = (3/13)i − (4/13)j + (12/13)k. Given a vector field F = xi + yj + zk, evaluate F at point (2, −1, 3). a) 2i − j + 3k b) i + j + k c) 3i − 2j + k d) 2i + j + 3k