Math Exercises: Analytic Geometry of the Straight Line and Plane 
Find the direction vector and the normal vector of a straight line p, if :
Find the parametric, the general and the slopeintercept equation of a straight line p passing through the points :
A straight line p with a direction vector d and a normal vector n passes through the point K. Find the parametric, the general and the slopeintercept equation of a straight line p, if :
Find the parametric, the general and the slopeintercept equation of a straight line p, which passes through the point M, if the slope angle between a straight line p and the xaxis is φ :
Transform the parametric equations of the straight line into the general equation and into the slopeintercept equation :
Transform the general equation of the straight line into the parametric equations and into the slopeintercept equation :
Transform the slopeintercept equation of the straight line into the parametric equations and into the general equation :
Find the general equation and the slopeintercept equation of a straight line, which passes through the point L and which is parallel to the given straight line p :
Find the general equation and the slopeintercept equation of a straight line, which passes through the point N and which is perpendicular to the given straight line p :
Find the slope angle of a straight line given by the equation :
Decide whether the given straight lines p and q are parallel or perpendicular to each other :
Consider the two points A [3;2], B [–1;–1] and the vector a = (12;–5), where a = C – B.
Find the general equation of the perpendicular bisectors of line segments AB, AC and BC, if A [2;5], B [–3;9], C [6;12].
Prove that the points A [3;4], B [–1;2], C [1;3], D [–5;0] lie on one straight line. Find the parametric, the general and the slopeintercept equation of the straight line.
Find the parametric equations of a straight line passing through the point A [4;–1;9] which is parallel to
Find the parametric equations of a straight line p passing through the point A [2;–1;2] perpendicularly to the plane π: x – y + z + 13 = 0.
Find the parametric equations and the general equation of a plane ρ = ABC, A [–4;0;2], B [–2;1;1], C [1;–3;–2].
Find the general equation of a plane α which passes through the point A [2;1;4] and which is parallel to the plane β: x – 2y + 5z + d = 0.
Find the general equation of a plane σ which passes through the point A [1;2;0] and which is perpendicular to the straight line p: x = 3 – t; y = 4 + 2t; z = 1 – 2t; t∈R.
Consider a regular square pyramid ABCDV with vertices D [0;0;0], A [4;0;0], B [4;4;0], V [2;2;6]. Find the general equation of a plane BCV.
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