Exam Exam

1.-(PAEG- June 2013) Study, depending of the value of a€R, the relative position of the plane π and the straight line r, where: a) if a = 5 parallel ones, if a ≠ 5 intersecting ones b) if a = -5 parallel ones, if a ≠ -5 intersecting ones c) if a = -5 r into π, if a ≠ -5 intersecting ones d) None of them

2.- (PAEG- june 2013) Study the relative position of the straight lines: a) Coincident lines b) Skew lines c) Intersecting lines d) Parallel lines

3.- (PAEG- September 2013) Study, depending of the value of a, the relative position of the straight lines: a) if a = -4 intersecting lines, if a ≠ -4 skew lines b) if a = -4 coincident lines, if a ≠ -4 parallel lines c) if a = 4 intersecting lines, if a ≠ 4 skew lines d) None of them

4.- Find the intersecting point from the exercise 3 in the case that they are intersecting

 a) (0,-3/2,1/2) b) (0,3/2,1/2) c) (0,3/2,-1/2) d) They aren't intersecting

5.- (PAEG Reserve1- 2013) Let the point P(1,0,1) and the straight line: Find the parametric equations of the line s that passes through the point P and intersects perpendicularly to r.

 a) b) c) d) 6.- Calculate the symmetric point of the point P from the line r from the exercise 5

 a) (5/3,4/3,0) b) (-5/3,4/3,7/3) c) (3,0,3) d) (-1,1/4,-3/4)

7.- (PAEG Reserve2- 2013) Let the plane π and the straight line r: Study their relative position

 a) Parallel ones b) Intersecting ones c) r into π d) Perpendicular ones

8.- Explain, in a reasoned way, how many planes there are that are perpendicular to π and contain r from exercise 7

 a) 0 b) 1 c) 2 d) ∞

9.- (PAEG Reserve2- 2013) Determine the value of kR to make that the straight line: is into the plane π: x + 2y + z - 7 = 0

 a) k = 0 b) k = -1/3 c) k = -12/5 d) k = 3

10.- For the value of k obtained from the exercise 9, find the implicit equation of a plane π' that is perpendicular to π and so that the intersection of the two planes is r.

 a) π': x - z - 3 = 0 b) π': x - y - z + 3 = 0 c) π': x - z - 1 = 0 d) π': 2y - z - 11 = 0