Linear Algebra Worksheet

Two points in space are represented by the position vectors A = (3, -2, 1) and B = (1, 4, -2). What is the distance between the two points?

• 6

• 7

• 17

• 49

The components of vector A are given as follows: Ax = 10.5 and Ay = 15.2. What is the magnitude of the vector?

• 10.5

• 15.2

• 18.5

• 4.7

Vectors A and B have magnitudes of 3 units and 4 units, what is the magnitude of A + B?

• srqt of 5 units

• 7 units

• sqrt of 7 units

• 5 units

Two vectors are given as follows: A = -2i - 5j + 2k and B = -4i - 2j - 3k. What is the angle between the vectors?

• 67

• 114

• 94

• 41

Two vectors are given as follows: A = -3i + 6j - 5k and B = -2i + 3j + k. The vector dot product is:

• 14

• 19

• -12

• 10

If r = 2, A = (2, 4) and B = (-5, 3), what is r (A + B)?

• (6, 14)

• (6, -14)

• (-6, -14)

• (-6, 14)

If two vectors A and B are equal where A = (2x, 4) and B = (6, 2y), what would be the value of x and y respectively.

• (1/3, 2)

• (1/3, ½)

• (3, 2)

• (3, ½)

Which of the following two vectors can be considered as orthogonal?

• none of these

• (-2,8) and (8, 2)

• (2, 8) and (8, 2)

• (-2, -8) and (-8, -2)

Given X = 2i + j + 2k, Y = 3i - j - 3k, and Z = i + 2j + 3k, find (X x Y) Z.

• 3i - 12j + 7k

• -i - 4j + 3k

• 8

• 9

Which of the following is not a property of a subspace (H) of a vector V?

• There should be -V in H.

• The zero vector, 0, of V is in H.

• H is closed under vector addition. That is, for each u and v in H, the sum u + v is in H.

• H is closed under multiplication by scalars. That is, for each u in H and each scalar c, the vector cu is in H.