SUMMARY
The coordinates of point C in parallelogram ABCD can be determined using vector addition based on the given vertices A(-1, 2, -1), B(2, -1, 3), and D(-3, 1, -3). The relationship A - B = D - C establishes that C can be calculated as C = D + (B - A). Substituting the values yields C = (-3, 1, -3) + ((2, -1, 3) - (-1, 2, -1)), resulting in C = (0, 4, 5). This method effectively utilizes the properties of parallelograms to find the unknown vertex.
PREREQUISITES
- Understanding of vector addition in three-dimensional space
- Familiarity with the properties of parallelograms
- Basic knowledge of coordinate geometry
- Ability to manipulate and solve equations involving vectors
NEXT STEPS
- Study vector addition and subtraction in R^3
- Explore the properties of parallelograms and their geometric implications
- Learn how to derive coordinates of unknown vertices in polygons
- Practice solving problems involving vector equations and geometric shapes
USEFUL FOR
Students studying geometry, mathematics educators, and anyone interested in understanding vector operations and their applications in three-dimensional space.