SUMMARY
The magnitude of the sum of the vectors A = i + 5j - k, B = 4i - j - 5k, and C = -i + j is calculated by first summing the components. The correct component addition yields 4i + 6j - 6k. The magnitude is then computed using the formula √(x² + y² + z²), resulting in √(4² + 6² + (-6)²) = √(16 + 36 + 36) = √88, which simplifies to approximately 9.38. The initial calculation error stemmed from incorrect component addition.
PREREQUISITES
- Vector addition in three-dimensional space
- Understanding of unit vectors i, j, k
- Knowledge of the magnitude formula for vectors
- Basic algebra for component calculations
NEXT STEPS
- Review vector addition techniques in three dimensions
- Study the properties of unit vectors i, j, k
- Practice calculating magnitudes of vectors using the formula √(x² + y² + z²)
- Explore common mistakes in vector addition and magnitude calculations
USEFUL FOR
Students studying physics or mathematics, particularly those learning about vector operations and their applications in three-dimensional space.