Mathematics
Mathematics
Problem
If the triangle ABC whose vertices are A (-1, 1, 1), B (1, -1, 1) and C (1, 1, -1) is projected on xy-plane, then the area of the projected triangles is .....Intuitive explanation
When you project a 3D triangle onto a plane, you're essentially looking at its "shadow"—the area shrinks by a factor equal to the cosine of the angle between the triangle's plane and the projection plane. The key is finding the normal vector to triangle ABC, then using the dot product with the xy-plane's normal to find that angle. Once you have , multiply the original triangle's area by this factor to get the projected area.
Intuitive explanation
When you project a 3D triangle onto a plane, you're essentially looking at its "shadow"—the area shrinks by a factor equal to the cosine of the angle between the triangle's plane and the projection plane. The key is finding the normal vector to triangle ABC, then using the dot product with the xy-plane's normal to find that angle. Once you have , multiply the original triangle's area by this factor to get the projected area.