Question 1

A vector A has a magnitude |A| and makes an angle$\theta$with respect to the y axis in a two-dimensional rectangular coordinate system. Ax is

Accepted Answer

A)  |A| sin $\theta$. 
B)  |A| cos $\theta$. 
C)  |A| tan$\theta$. 
D)  none of the above. 
A)  |A| sin $\theta$. 
B)  |A| cos $\theta$. 
C)  |A| tan$\theta$. 
D)  none of the above.

Question 2

Consider vectors A and B (not parallel to each other). In a rotated coordinate system (compared to an original coordinate system), all of the following remain unchanged except

Accepted Answer

A)  A · B. 
B)  A $\times$ B. 
C)  |A| and |B|. 
D)  the components of A and the components of B. 
A)  A · B. 
B)  A $\times$ B. 
C)  |A| and |B|. 
D)  the components of A and the components of B.

Question 3

All of the following combinations of vectors A, B, and C are vectors except

Accepted Answer

A)  A + B + C. 
B)  (A · 
B) C. 
C)  A · B $\times$ C. 
D)  A $\times$ B. 
A)  A + B + C. 
B)  (A · 
B) C. 
C)  A · B $\times$ C. 
D)  A $\times$ B.

Question 4

If A = -i + 2j + k and B = i + j + 2k, the angle between vectors A and B is

Accepted Answer

A)  53°. 
B)  30°. 
C)  37°. 
D)  60°. 
A)  53°. 
B)  30°. 
C)  37°. 
D)  60°.

Question 5

The angle between two vectors is equal to the (smallest) angle between their lengths when they are joined in all of the following ways except

Accepted Answer

A)  tail to tail. 
B)  head to head. 
C)  head to tail. 
D)  Hold it! There are no exceptions. 
A)  tail to tail. 
B)  head to head. 
C)  head to tail. 
D)  Hold it! There are no exceptions.

Question 6

If A = 4i - 2j + 3k and B = 2i + j - 2k, the angle between vector A and vector B is

Accepted Answer

A)  0°. 
B)  45°. 
C)  -45°. 
D)  90°. 
A)  0°. 
B)  45°. 
C)  -45°. 
D)  90°.

Question 7

If A = 2i - 2j - k and B = i + 2j - 2k, the area of a parallelogram whose sides are defined by vectors A and B is

Accepted Answer

A)  0. 
B)  3. 
C)  6. 
D)  9. 
A)  0. 
B)  3. 
C)  6. 
D)  9.

Question 8

A vector A has a magnitude of 3.0 units and makes an angle of 30° with the + x axis in a two-dimensional rectangular coordinate system. Ay is equal to

Accepted Answer

A)  1.5 units. 
B)  -1.5 units. 
C)  2.6 units. 
D)  -2.6 units. 
A)  1.5 units. 
B)  -1.5 units. 
C)  2.6 units. 
D)  -2.6 units.

Question 9

A vector A has the components Ax = 3.0 and Ay = 4.0. The magnitude of A is

Accepted Answer

A)  1.0. 
B)  3.5. 
C)  5.0. 
D)  7.0. 
A)  1.0. 
B)  3.5. 
C)  5.0. 
D)  7.0.

Question 10

Let vector A = 3.0i + 2.0j. A new rectangular coordinate system is generated by a 45° counterclockwise rotation about the k axis. Vector A in the new coordinate system is given by

Accepted Answer

A)  3.5i - 0.71j. 
B)  2.0i + 3.0j. 
C)  3.5i + 0.71j. 
D)  2.0i - 3.0j. 
A)  3.5i - 0.71j. 
B)  2.0i + 3.0j. 
C)  3.5i + 0.71j. 
D)  2.0i - 3.0j.

Exam 3: Vectors

A vector A has a magnitude |A| and makes an angle θ\thetaθ with respect to the y axis in a two-dimensional rectangular coordinate system. Ax is

Consider vectors A and B (not parallel to each other). In a rotated coordinate system (compared to an original coordinate system), all of the following remain unchanged except

All of the following combinations of vectors A, B, and C are vectors except

If A = -i + 2j + k and B = i + j + 2k, the angle between vectors A and B is

The angle between two vectors is equal to the (smallest) angle between their lengths when they are joined in all of the following ways except

If A = 4i - 2j + 3k and B = 2i + j - 2k, the angle between vector A and vector B is

If A = 2i - 2j - k and B = i + 2j - 2k, the area of a parallelogram whose sides are defined by vectors A and B is

A vector A has a magnitude of 3.0 units and makes an angle of 30° with the + x axis in a two-dimensional rectangular coordinate system. Ay is equal to

A vector A has the components Ax = 3.0 and Ay = 4.0. The magnitude of A is

Let vector A = 3.0i + 2.0j. A new rectangular coordinate system is generated by a 45° counterclockwise rotation about the k axis. Vector A in the new coordinate system is given by

Space, Time, and Mass

Motion Along a Straight Line

Motion in Two and Three Dimensions

Newtons Laws of Motion

Further Applications of Newtons Laws

Work and Energy

Conservation of Energy

Gravitation

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Rotation of a Rigid Body

Dynamics of a Rigid Body

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The Ideal Gas

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The Electric Field

Gauss Law

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The Theory of Special Relativity

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Nuclei

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Filters

A vector A has a magnitude |A| and makes an angle $\theta$ with respect to the y axis in a two-dimensional rectangular coordinate system. A_xis

A vector A has a magnitude of 3.0 units and makes an angle of 30° with the + x axis in a two-dimensional rectangular coordinate system. A_y is equal to

A vector A has the components A_x = 3.0 and A_y = 4.0. The magnitude of A is