10.1.3 Formulas in Three Dimensions

Question 1

polyhedron

Answer 1

formed by four or more polygons that intersect only at their edges

Question 2

Space

Answer 2

the set of all points in three dimensions

Question 3

Euler’s Formula

Answer 3

For any polyhedron with V vertices, E edges, and F faces, V − E + F = 2

Question 4

Diagonal of a Right Rectangular Prism

Answer 4

The length of a diagonal of a right rectangular prism with length , width w, and height h is d = √l^2 + w^2 + h^2

Question 5

Distance Formula in Three Dimensions

Answer 5

he distance between the points (x1, y1, z1) and (x2, y2, z2) is d = √(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2

Question 6

Midpoint Formula in Three Dimensions

Answer 6

The midpoint of the segment with endpoints (x1, y1, z1) and (x2, y2, z2) is M(x1+x2/2, y1+y2/2, z1+z2/2)