List of top Mathematics Questions on 3D Geometry

The volume of the tetrahedron with vertices \( P(1, 2, 0), Q(2, 1, -3), R(1, 0, 1) \), and \( S(3, -2, 3) \) is:

An equation of the plane passing through the line of intersection of the planes \( x + y + z = 6 \) and \( 2x + 3y + 4z = 5 \), and passing through \( (1, 1, 1) \) is:

The length of the shortest distance between the lines \( \mathbf{r} = 3i + 5j + 7k + \lambda(2i - 2j + 3k) \) and \( \mathbf{r} = -i - j + k + \mu(7i - 6j + k) \) is:

Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\