VECTORES

VECTORES
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) If A + B = C and their magnitudes are given by A + B = C, then the vectors A and B are oriented
A) parallel to each other (in the same direction).
B) perpendicular relative to one other.
C) antiparallel to each other (in opposite directions).
D) It is impossible to know from the given information.
1)
2) The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between
these two vectors is
A) 270°
B) 180°
C) 90°
D) 0°
E) 60°
2)
3) Vectors M and N obey the equation M + N = 0. These vectors satisfy which one of the following
statements?
3)
A) Vectors M and N point in the same direction.
B) Vectors M and N are at right angles to each other.
C) Vectors M and N have the same magnitudes.
D) The magnitude of M is the negative of the magnitude of N .
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) Refer to the figure, which shows four vectors M , N , S , and T .
(a) Vector S as expressed in terms of vectors M and N is given by
A) M + N .
B) M - N .
C) N - M .
4)
5) Refer to the figure, which shows four vectors M , N , S , and T .
5)
Vector T as expressed in terms of vectors M and N is given by
A) M + N .
B) M - N .
C) N - M .
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
6) Consider two vectors A and B shown in the figure. The difference A - B is best illustrated by
A) choice (a)
B) choice (b)
C) choice (c)
6)
D) choice (d)
7) The eastward component of vector A is equal to the westward component of vector B and their
northward components are equal. Which one of the following statements must be correct for these
two vectors?
7)
A) Vector A is antiparallel (in the opposite direction) to vector B .
B) The angle between vector A and vector B must be 90°.
C) The magnitude of vector A must be equal to the magnitude of vector B .
D) Vector A must be perpendicular to vector B .
E) Vector A is parallel to vector B .
8) The x component of vector A is 8.7 units, and its y component is -6.5 units. The magnitude of A is
closest to
A) 9.9 units
B) 8.9 units
C) 12 units
D) 7.9 units
E) 11 units
8)
9) When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was
1.8 m/s. What was the angle of the mountain surface above the horizontal?
A) 33°
B) 75°
C) 15°
D) 57 °
9)
10) A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the
displacement of the football?
A) 55.0 m
B) 74.0 m
C) 64.7m
D) 24.2 m
E) 0.00 m
10)
11) A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What
is the horizontal component of the boy's velocity?
A) 12.6 m/s
B) 9.33 m/s
C) 15.6 m/s
D) 18.1 m/s
E) 8.45 m/s
11)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
12) Shown below are the velocity and acceleration vectors for an object in several different
types of motion. In which case is the object slowing down and turning to its right?
12)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
13) The magnitude of A is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 °
13)
with the +y-axis. The components of A are closest to:
A) Ax = -3.1 m, Ay = 4.6 m.
B) Ax = -4.6 m, Ay = -3.1 m.
C) Ax = -4.6 m, Ay = 3.1 m.
D) Ax = 3.1 m, Ay = -4.6 m.
E) Ax = 4.6 m, Ay = -3.1 m.
14) The components of vectors B and C are given as follows:
Bx = -9.2
By = -6.1
14)
Cx = -4.5
Cy = 4.3
The angle (less than 180°) between vectors B and C is closest to
A) 103°.
B) 84°.
C) 170°.
D) 10°.
E) 77°.
15) The components of vectors A and B are given as follows:
Ax = 7.6
Bx = -5.1
Ay = -9.2
15)
By = -6.8
What is the magnitude of the vector difference B - A ?
A) 170
B) 13
C) 3.4
D) 3.5
E) 16
16) Three forces, F 1, F 2, and F 3 , each of magnitude 70 N, all act on an object as shown in the figure.
The magnitude of the resultant force acting on the object is
A) 70 N.
B) 210 N.
C) 35 N.
D) 0 N.
E) 140 N.
17) Three vectors, S , T , and U , have the components shown in the table. What is the magnitude of
the resultant of these three vectors?
x component
y component
S
3.50 m
-4.50 m
T
2.00 m
0.00 m
U
-5.50 m
2.50 m
A) 5.50 m
B) 2.00 m
C) 11.1 m
D) 7.00 m
19) Un vector está dado como sigue:
C = -5 i -2 j - 3 k
El vector producto C × J es igual a:
B) -3 i - 2 j + 5 k
C) +3 i - 5 k
D) +3 i + 5 k
E) -3 i + 5 k
18)
B = -2 i - 5 j + 2 k
El producto escalar A · B corresponde a:
A) -12
B) -20
C) 8
A) +3 i + 2 j - 5 k
17)
E) 13.0 m
18) Dos vectores se dan como sigue:
A = +3 i - 2 j - 2 k
16)
D) 12
E) cero
19)
20) ¿Cuál de las afirmaciones siguientes es correcta?
A) Si los vectores A y B son rotados cada uno con el mismo ángulo del mismo eje, el producto
A · B no se alterará.
B) Cuando una cantidad escalar es adicionada a un vector, la resultante es un vector de mayor
magnuitud que el vector original.
C) Si los vectores A y B son rotados cada uno con el mismo ángulo del mismo eje, el producto
A x B no se alterará.
D) Si los vectores A y B son rotados ambos con el mismo ángulo sobre el eje, la suma de A + B
no cambiará.
E) Si un vector A se rota sobre un eje paralelo al B, el producto A · B puede cambiar.
20)