  ### Math Exercises & Math Problems: Relative Position, Distance and Deviation Between Points, Lines and Planes  Find the distance between two points :  Find the distance from a point to a straight line :  Find the distance from a point to a plane :  Determine the relative position of the given straight lines, calculate the angle between them and find the intersection of the straight lines (if any exists) :  Determine the relative position of the straight line and the plane, calculate the angle between them and find their intersection (if any exists) :  Determine the relative position of the given planes, calculate the angle between them and find the intersection of the planes (if any exists) :  Determine the relative position of three planes :  Find the distance between two straight lines p: 3x – 4y – 20 = 0 and q: 6x – 8y + 25 = 0. Find the distance between a straight line p: {x = 2t – 1; y = 1 – t; z = 2 + 3t; t∈R} and a planeρ: x + 5y + z – 3 = 0. Find the distance between two planes α: 2x + y + 3z + 1 = 0 and β: 6x + 3y + 9z + 5 = 0. Find the general equation of a straight line that passes through the point M [15;–3] and through the intersection of the straight lines p: 3x – 5y + 12 = 0 and q: 5x + 2y – 42 = 0. Find the general equation of a straight line that passes through the point A [3;–2], if the size of an angle between the unknown straight line and the straight line p: x – y + 1 = 0 is α = 30°. Find the general equation of a straight line that passes through the point A [2;3], if the distance from a point B [0;–1] to the unknown straight line is d = 4. Find the image of a point A [1;0;2] under the plane symmetry given by the plane β: x – 2y + 3z – 21 = 0. Two sides of a parallelogram lie on straight lines 8x + 3y + 1 = 0, 2x + y – 1 = 0 and the diagonal of a parallelogram lies on a straight line 3x + 2y + 3 = 0. Find the coordinates of vertices of a parallelogram. Find the size of internal angles of the triangle ABC, if A [4;0;6], B [6;–3;12], C [10;2;3]. Two vertices of a triangle ABC have coordinates A [–10;2], B [6;4] and the orthocenter of a triangle is O [5;2]. Find the coordinates of a vertex C. Sides of a triangle lie on straight lines a: 3x + 4y – 1 = 0, b: x – 7y – 17 = 0, c: 7x + y + 31 = 0. Find the coordinates of vertices A, B, C of a triangle. Vertices of a regular tetrahedron have the coordinates A [6;0;0], B [0;5;0], C [5;6;0], D [2;3;8]. Find the angle between straight lines AB, CD and the angle between a straight line CD and a plane ABD. Consider a regular square pyramid ABCDE whose base lies on the xy-plane, A [0;0;0], B [5;0;0], D [0;5;0] and the vertical height of a pyramid h = 7. a) Find the distance from a point A to a point C. b) Find the distance from a point A to a point E. c) Find the distance from a point E to a midpoint of the edge AB. d) Find the distance between midpoints of the edges AE and CE. e) Find the size of an angle between adjacent faces of the pyramid. f) Find the size of an angle between opposite faces of the pyramid. g) Find the size of an angle between straight lines BC and DE. h) Find the size of an angle between straight lines BE and DE. i) Find the size of an angle between a straight line AE and a plane ABC. j) Find the size of an angle between a straight line AE and a plane BCE.  You might be also interested in:  