NAME :
CLASS :
Vectors
DATE :
25 Questions
1.
Find the component form of AB with initial point A(1, -3)
and terminal point B(1, 3)
2.
a) <2, 0>
b) <0, 6>
c) 2i
d) 6j
Find the component form of AB with initial point A(0, 8) and
terminal point B(-9, -3)
a) -9i + 5j
b) -9i - 11j
c) <-9, -11>
d) <-9, 5>
a) The scalar product of v and w
b) Dot product of v and w
c) vector v times vector w
d) V x W
a) Direction of AB
b) Distance of vector AB
c) Vector AB
d) Magnitude of vector AB
3.
4.
5.
If w = <2, -5> and y = <2, 0>, nd 2w + y
a) <-10, 2>
b) <4, -5>
c) <-6, 10>
d) <6, -10>
6.
7.
8.
If y = <2, 0> and z = <-1, -4>, nd 3y - 2z
a) <5, -8>
b) <4, 8>
c) <8, 8>
d) <-8, -8>
Find the magnitude of AB if the initial point is (-3, 1) and the
terminal point is (3, 9)
a) 6
b) 8.2
c) 10
d) 10.4
Is this a scalar quantity or a vector quantity?
Wind blowing at 20 knots
a) Scalar
9.
b) Vector
Is this a scalar quantity or a vector quantity?
A 15-pound tire hanging from a rope
a) Scalar
10.
Is this a scalar quantity or a vector quantity?
A deer running 15 meters per second due west
a) Scalar
11.
12.
b) Vector
b) Vector
Are these two vectors equivalent? u = <3,6> and v = <-4,2>
a) Yes
b) No
c) How am I suppose to know?
d) Really, Ms. A... What is this?
Are these two vectors parallel? u = -i - 4j and v = 3i - 2j
a) Yes
b) No
c) Maybe
d) Huh?
13.
14.
Are these two vectors orthogonal? u = <2,4> and v = <-12,6>
a) Yes
b) No
c) Maybe
d) How do we do this again?
A quantity that has both magnitude and direction is called a
scalar quantity.
a) True
15.
b) False
What is the minimum (smallest) resultant possible when
adding a 3 unit vector and an 8 unit vector?
a) 24
b) 11
c) 8
d) 5
16.
the magnitude (or length) of u. If necessary, leave as a
square root.
a) √63
b) 3
c) √65
d) 9
the direction (θ) for vector v. Round to three decimals.
17.
a) -74.054o
b) 105.945o
c) -15.945o
d) 164.055o
18.
the angle between vectors u and v. Round to three
decimals.
a) 45o
b) 26.231o
c) 156.930o
d) 8.820o
19.
To add two vectors algebraically, add all the numbers in the
rst vector together. Then add all the numbers in the
second vector together.
a) True
20.
b) False
Find the component form of the vector. Round to three
decimals.
21.
a) <16.116, 7.798>
b) <16.298, 7.335>
c) <16.892, 7.530>
d) <16.314, 7.607>
An airplane is ying on a bearing of 340o at 355 mph. A
wind is blowing with the bearing of 115o at 40 mph. Find
the component form of the resultant vector (p + W). Round
to three decimal places.
22.
a) <-85.165, 316.686>
b) <316.686, -85.165>
c) <-316.686, -85.165>
d) <-89.543, 309.289>
If you have the points A(-4,7) and B(-10,23), nd the vector
AB.
a) <-6,16>
b) <16,-6>
c) <-14,30>
d) <30,-14>
23.
Find the unit vector in the same direction as v.
a) <0.385, 0.923>
b) <-0.832, 0.555>
c) <5/13, 12/13>
d) <-5/13, -12/13>
24.
Find cos ϴ (the ratio), where ϴ is the angle between
vectors a = i + j and b = -2i + 3j.
25.
a) 1 ⁄ √22
b) 1 ⁄ √24
c) 1 ⁄ √26
d) 1 ⁄ √28
Find the projection of u=<3,-12> onto v=<9,2>.
a) <27/85, 6/85>
b) <85/27, 85/6>
c) <9/85, -36/85>
d) <85/9, -85/36>
Answer Key
1.
b
8.
a
15.
d
22.
a
2.
c
9.
b
16.
c
23.
d
3.
b
10.
b
17.
b
24.
c
4.
d
11.
b
18.
d
25.
a
5.
6.
d
c
12.
13.
b
a
19.
20.
b
d
7.
c
14.
b
21.
b