SUMMARY
The cosine of the angle between the normals to the planes defined by the equations x+y+2z=3 and 2x-y+2z=5 can be calculated using the formula cos θ = V * W / ||V|| ||W||. The normal vectors for the given planes are derived directly from the coefficients of x, y, and z in the equations. For the first plane, the normal vector is (1, 1, 2), and for the second plane, it is (2, -1, 2). The next step involves calculating the dot product of these vectors and their magnitudes to find the cosine value.
PREREQUISITES
- Understanding of vector mathematics
- Familiarity with normal vectors in three-dimensional space
- Knowledge of the dot product and vector magnitudes
- Basic algebra for manipulating equations
NEXT STEPS
- Study the concept of normal vectors in 3D geometry
- Learn how to calculate the dot product of two vectors
- Explore vector magnitude calculations
- Review applications of cosine in angle calculations between vectors
USEFUL FOR
Students in geometry or linear algebra, mathematics enthusiasts, and anyone looking to understand the relationship between planes and their normals in three-dimensional space.