Math Exercises: Metric Relations in Space 
Consider a cube ABCDEFGH, AB = a = 4 cm. Find the distance from a point F to a given straight line :
Consider a cuboid ABCDEFGH, AB = a = 60 cm, AD = b = 400 mm, AE = c = 8 dm. Find the distance from a point B to a point H, distance from a point D to a point G and the distance from a point C to a point F.
Consider a cone with a base diameter of d = 12 cm. Any point on the circumference of the base is located 8.5 cm from the apex of the cone. Find the distance from the apex V to the base.
Consider a truncated pyramid ABCDEFGH with square bases. Find the distance between planes ABCD and EFGH, if you know AC = 13 cm, FH = 9 cm and AG = 15 cm.
Consider a triangular prism ABCDEF with a base of right triangle, which has the right angles at the vertices C and F. The lengths of legs are AC = 8 m, BC = 6 m and a height of the prism is h = 15 m. Find the distance between points E and S and the size of an angle φ = ∠BSE, where S is the midpoint of an edge AC.
Consider a cube ABCDEFGH with the points on its edges X∈EH, Y∈AB, Z∈GH, if we know EH = XH, AY = YB, ZH = 3GZ. Find the angle between the straight lines AX and YZ.
Consider a cube ABCDEFGH. Let M be a midpoint of an edge AE and the size of a cube's edge is a. Find the angle between the straight lines BH and BM.
Consider a regular square pyramid ABCDV, AB = a, AV = a. Find the angle between two adjacent slant faces of the pyramid.
Consider a cube ABCDEFGH. Find out whether the planes DBH and ACF are perpendicular to each other.
Consider a regular hexagonal pyramid ABCDEFV, where AB = a, AV = 2a and a point M is the midpoint of the edge AV. Find the distance from the point M to the straight line DV.
Consider a cuboid ABCDEFGH. Find the distance from the straight line AC to the straight line FH and the volume of a cuboid, if AG = 5, AC = 3, AH = .
Consider a cube ABCDEFGH, where AB = a = 5 cm, point M is the midpoint of the edge EF, point K is the midpoint of the edge CD. Find the distance from the plane BMG to the plane HAK.
Consider a regular square pyramid ABCDV, where AB = a = 4 cm, AV = b = 6 cm. Find the angle between two planes BCV and ABC.
Consider a cube ABCDEFGH, let a point K be the midpoint of the edge FG. Find out whether the planes ADK and DCH are perpendicular to each other.
Consider a regular tetrahedron ABCD, AB = a. Find the distance between two straight lines on which lie opposite edges of the tetrahedron.
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