# Exam

Exam

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 R3 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) d) None of them

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) d) None of them

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

 a) 64o45'38 b) 112o23'23'' c) 154o45'38'' d) None of them

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) 3u2 b) 6u2 c) √3u2 d) √6u2

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) -3u3 b) 9u3 c) 3u3 d) 0u3

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)u3 b) (3/2)u3 c) (1/2)u3 d) 0u3