Final answer:
To find vector B, which is orthogonal to vector A = 3i + 4j and has the same magnitude, we can use the orthogonality and equal magnitude conditions. One possible solution for Vector B is -4i + 3j.
Step-by-step explanation:
Given that vector A and vector B are orthogonal vectors in the xy-plane and have equal magnitudes, and also given that Vector A = 3i + 4j, we can find Vector B by ensuring its dot product with Vector A is zero (because they are orthogonal) and that it has the same magnitude as Vector A.
The magnitude of Vector A is √(3² + 4²) = 5.
Since Vector B must have the same magnitude and be orthogonal to A, its components must satisfy the equations Bx * 3 + By * 4 = 0 (orthogonality condition) and √(Bx² + By²) = 5 (equal magnitude condition).
One possible solution for Vector B is -4i + 3j, since (-4) * 3 + 3 * 4 = 0 and √((-4)² + 3²) = 5.