1.- Decide which of the following sentences is true:

a) All the generative systems are bases

b) All the sets of linearly independent vectors are bases

c) A set of three linearly independent vectors in R^{3} is a basis

d) All of the sentences are true

2.- Let u(1,3,1) and v(-1,0,-2). Then 3u-2v =

a) (5,9,7)

b) (1,9,-1)

c) (3,1,-2)

d) None of them

3.- Let A(1,4,2), B(1,3,2), C(4,7,3). Find the coordinates of the point D that makes ABCD a parallelogram.

a) (4,8,3)

b) (4,6,3)

c) (1,5,2)

4.- Let u(-1,1,0) and v(3,-3,2). Find the orthogonal projection of u over v.

a) (3/11,-3/11,0)

b) (-9/11,9/11,-6/11)

c) (9/11,-9/11,6/11)

5.- Let u(-1,1,0) and v(3,-3,2). Find the angle between u and v.

a) 64^{o}45'38

b) 112^{o}23'23''

c) 154^{o}45'38''

6.- Let u(1,-1,0) and v(1,0,-2). Find w, a vector orthogonal to u and v with |w|= 6.

a) (2,2,1)

b) (4,4,-2)

c) (4,-4,2)

d) (4,4,2)

7.- Let u(1,-1,0) and v(1,0,-2). Calculate the area of the parallelogram defined by u and v.

a) 3u^{2}

b) 6u^{2}

c) √3u^{2}

d) √6u^{2}

8.- Calculate (u,v,w) where u(0,-1,2), v(1,3,-2), w(1,-1,3)

a) 3

b) -9

c) 0

d) -3

9.- Calculate the volume of the parallelepiped defined by u, v and w, where u(0,-1,2), v(1,3,-2), w(1,-1,3)

a) -3u^{3}

b) 9u^{3}

c) 3u^{3}

d) 0u^{3}

10.-Calculate the volume of the tetrahedron defined by u, v and w, where u(0,-1,2), v(1,3,-2), w(1,-1,3)

a) (-1/2)u^{3}

b) (3/2)u^{3}

c) (1/2)u^{3}

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