Exercises for Homework 3

Date: 2015-10-07; view: 444.

3.14. Compose an equation of the plane passing through the point and that is parallel to the plane: a) ; b) ; c) .

3.15. Compose an equation of the line passing through the point and that is parallel to the line: a) ; b) ; c) .

3.16. Compose an equation of the line passing through two given points:

a) and ; b) and .

3.17. Compose an equation of the plane passing through three given points (if these points determine a plane): a) , and ; b) , and ; c) , and .

3.18. 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 .

3.19. For which the planes and are: a) intersecting; b) parallel; c) coinciding?

3.20. 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) ;