Shortcut Methods
JEE Mains:
Heights and Distances:
- Use trigonometric ratios to find heights and distances.
- Similar triangles can be helpful.
Direction Cosines:
- Represent the direction of a line in 3D space.
- Find direction cosines, angles between lines.
Planes:
- Find equations of planes, intersections, distances.
Lines and Planes:
- Determine angles, parallelism/perpendicularity, intersection points.
Spheres:
- Find equations, intersection with planes, volume.
Cones and Cylinders:
- Calculate surface areas, volumes, intersections.
Coordinate Geometry in 3D:
- Find distances, equations, 3D solid volumes.
CBSE Board Exams:
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Similar to JEE Mains, slightly less difficult.
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Finding building heights with trigonometry.
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Distance between points using distance formula.
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Plane equations through three points.
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Angles between lines using direction cosines.
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Volume calculations for spheres and cylinders.
Practice variations of numerical problems to excel.
