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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