கணிதம் உங்களுக்காக - 17 - கான்ஸெப்ட்கள்

 1. Equation of a plane in normal form: n₁x + n₂y + n₃z = d (where (n₁, n₂, n₃) is the normal vector and d is the perpendicular distance from the origin)

2. Distance from a point to a plane: d = |Ax₁ + By₁ + Cz₁ + D| / √(A² + B² + C²)

3. Angle between two planes: cos(θ) = |n₁ · n₂| / (|n₁| |n₂|) (where n₁ and n₂ are the normal vectors of the planes)

4. Intersection of two planes: The line of intersection can be found by solving the system of equations of the planes.

5. Distance between two parallel planes: d = |D₁ - D₂| / √(A² + B² + C²) (where Ax + By + Cz + D₁ = 0 and Ax + By + Cz + D₂ = 0 are the equations of the planes)

6. Central angle theorem: The measure of the central angle is equal to the measure of the intercepted arc.

7. Inscribed angle theorem: The measure of an inscribed angle is half the measure of its intercepted arc.

8. Angle between a tangent and a chord: The measure of the angle formed by a tangent and a chord is half the measure of the intercepted arc.

9. Alternate segment theorem: The angle between the tangent and a chord through the point of contact is equal to the angle in the alternate segment.

10. Reflection over the origin: (x, y) → (-x, -y)

11. Reflection over the line y = -x: (x, y) → (-y, -x)

12. Rotation by 90 degrees counterclockwise around the origin: (x', y') = (-y, x)

13. Rotation by 180 degrees around the origin: (x', y') = (-x, -y)

14. Rotation by 270 degrees counterclockwise around the origin: (x', y') = (y, -x)

15. Area of an equilateral triangle: A = (√3 / 4) a² (where a is the side length)

16. Perimeter of an equilateral triangle: P = 3a (where a is the side length)

17. Area of a rhombus: A = ½(d₁d₂) (where d₁ and d₂ are the lengths of the diagonals)

18. Perimeter of a rhombus: P = 4a (where a is the side length)

19. Area of a trapezoid: A = ½(a + b)h (where a and b are the lengths of the parallel sides and h is the height)

20. Perimeter of a trapezoid: P = a + b + c + d (where a, b, c, and d are the lengths of the sides)

21. Sum of the exterior angles of a polygon: 360°

22. Number of diagonals in a polygon: n(n - 3) / 2 (where n is the number of sides)

23. Measure of each interior angle of a regular polygon: (n - 2) × 180° / n

24. Measure of each exterior angle of a regular polygon: 360° / n

25. Area of a regular polygon: A = ½ × Perimeter × Apothem (where Perimeter = n × s, n is the number of sides, s is the side length, and the Apothem is the perpendicular distance from the center to a side)