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)
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) 64o45'38
b) 112o23'23''
c) 154o45'38''
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) 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
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