Q1) What are the values of the angles in the figure
below?
1) o= o
2) o=o
3) o= o
4) o= o
5) none of the above

12
4

Q2) Three sticks are arranged to form a right triangle. If the lengths
of the three sticks are 0.47 m, 0.62 m and 0.78 m, what are the
three angles of the triangle?
1) 90°, 45°, and 45°
2) 90°, 59°, and 31°
3) 90°, 62°, and 28°
4) 90°, 48°, and 42°
5) 90°, 53°, and 37°
Q3) Vector A points along the +y axis and has a magnitude of 100.0 units.
Vector B points at an angle of 60.0o above the +x axis and has a
magnitude of 200.0 units. Vector C points along the +x axis and has a
magnitude of 150.0 units. Which vector has (a) the largest x component
and (b) the largest y component?
1)
2)
3)
4)
5)
(a) Vector A
(a) Vector B
(a) Vector B
(a) Vector C
(a) Vector C
(b) Vector B
(b) Vector C
(b) Vector A
(b) Vector B
(b) Vector A
Q4) The solid line has length A and makes an angle  with the
negative y-axis. What is the length of the dotted line?
y
1) A cos
2) A sin
3) A tan
4) sin/A
5) cos/A
x
A

Q5) What is the correct formula for Ay, the y-component of the
vector A?
y
1)
2)
3)
4)
5)
A cos
A sin
-A cos
-A sin
None of these.

x
A
Q6) Which of the following statements are true?
1) A vector can have a positive or negative magnitude.
2) A vector’s magnitude cannot be more than the magnitude
of one of its components.
3) The magnitude of a vector cannot be zero unless all of its
components are zero.
4) two of the above
5) none of the above
Q7) A physics student adds two displacement vectors with
magnitudes of 8.0 km and 6.0 km. Which one of the following
statements is true concerning the magnitude of the resultant
displacement?
1) It must be 10.0 km.
2) It must be 14.0 km.
3) It could be zero km, depending on how the vectors are oriented.
4) No conclusion can be reached w/o knowing the directions.
5) It could have any value between 2.0 km and 14.0 km.
Q8) Can two vectors of unequal magnitude sum to zero?
1) Yes.
2) No.
Q9) What is the minimum number of vectors with unequal
magnitudes whose vector sum can be zero?
1) two
2) three
3) four
4) five
5) six
Q10) Can the magnitude of the difference
between two vectors ever be greater than the
magnitude of their sum?
1) yes
2) no
Q11) Two vectors A and B are added together to form a vector C.
The relationship between the magnitudes of the vectors is given by
A + B = C. Which one of the following statements concerning
these vectors is true?
1) A and B must be displacements.
2) A and B must have equal lengths.
3) A and B must point in opposite directions.
4) A and B must point in the same direction.
5) A and B must be at right angles to each other.
Q12) The x and y components of a displacement vector
are –3.00 m and +4.00 m, respectively. What angle
does this vector make with the +x axis?
1) 233o
2) 127o
3) –53.0o
4) 53.0o
5) 37.0o
Q13) Let A = (2.00 m)i + (6.00 m)j - (3.00m)k. The
magnitude of A is:
1) 5.00 m
2) 5.57 m
3) 7.00 m
4) 7.42 m
5) 8.54 m
Q14) The angle between A = (-25m)i + (45m)j and the +x axis is:
1) 29º
2) 61º
3) 119º
4) 151º
5) 209º
Q15) Vector A has components Ax = +5 m and Ay = -10 m.
Vector B has components Bx = +45 m and By = +20 m. What is the
magnitude of A – B?
1) 30 m
2) 40 m
3) 50 m
4) –50 m
5) –70 m
Q16) A vector F1 has a magnitude of 40.0 units and points 35.0°
above the positive x axis. A second vector F2 has a magnitude of
65.0 units and points in the negative y direction. Use the
component method of vector addition to find the magnitude and
direction, relative to the positive x axis, of the resultant
F = F1 + F2.
1) 53.3 units, 52.1° below the +x axis
2) 53.3 units, 52.1° above the +x axis
3) 76.3 units, 37.9° below the +x axis
4) 76.3 units, 52.1° above the +x axis
5) 9.23 units, 37.9° below the +x axis
Q17) If A = 12i – 16j and B = -24i + 10j, what is the magnitude of
the vector C = 2A – B?
1) –49
2) –41
3) –90
4) +49
5) +221
Q18) The three forces shown act on a particle. What is the
magnitude of the resultant of these three forces?
y
1) 27 N
2) 33 N
3) 36 N
4) 24 N
5) 105 N
65 N
30º
30 N
20 º
20 N 0
x
Q19) Two vectors A and B, are added together to form the vector
C = A + B. The relationship between the magnitudes of these
vectors is given by: Cx = A cos 30° + B; Cy = –A sin 30°
Which statement best describes the orientation of these vectors?
1) A points in the -x direction while B points in the +y direction.
2) A points in the -y direction while B points in the +x direction.
3) A points 30° below the +x axis while B points in the +x direction.
4) A points 30° above the +x axis while B points in the +x direction.
5) A points 30° above the -x axis while B points in the +x direction.
Q20) The value of i · (j  k) is:
1) zero
2) +1
3) -1
4) 3
5) 3½
Q21) The value of k · (k  i) is:
1) zero
2) +1
3) -1
4) 3
5) 3½
Q22) If A = –2i + 3j and B = i + 2j, find the dot product of A and B.
1) –2
2) 1
3) 2
4) 3
5) 4
Q23) If A = 3.0i + 2.0j, B = 2.0i + 4.0j, and C = 4.0i + 3.0j, find
C  (A – B).
1)
2)
3)
4)
5)
–2
0
2
4
6