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

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 k€R 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

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