Exercises for Seminar 3 (plane in the space)
Date: 2015-10-07; view: 458.
3.1. a) Knowing the parametric equations of a plane: 
, compose its common equation; b) Knowing a common equation of the plane 
, compose their parametric equations.
3.2. a) Write equations of the line 
as an intersection of two planes and in canonical form; b) Write equations of the line 
in parametric and canonical forms.
3.3. Compose an equation of the plane passing through the point 
and that is parallel to the plane: a) 
; b) 
; c) 
.
3.4. Compose an equation of the line passing through the point 
and that is parallel to the line: a) 
; b) 
.
3.5. Compose an equation of the line passing through two given points: 
and 
.
3.6. Compose an equation of the plane passing through three given points (if these points determine a plane): a) 
, 
and 
; b) 
, 
and 
.
3.7. Two planes are given. Check whether they are intersecting, parallel or coinciding. If planes are intersected, compose canonical equations of the line of intersecting. The planes are given by the following equations: a) 
and 
;
b) 
and 
.
3.8. Check whether a given line lies in the plane 
, is parallel to this plane or intersects it in a unique point; in last case find the coordinates of the point of intersecting. A line is given by the following equations: a) 
; b) 
.
3.9. Compose an equation of the plane passing through the point and that is perpendicular to the line: a) 
; b) 
.
3.10. Find the distance between the point 
and the plane 
.
3.11. Find an angle between planes: 
and 
.
3.12. Find an angle between lines: 
and 
, 
.
3.13. Find an angle between the plane 
and the line 
, 
.
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