Scalars and vectors, vector addition and subtraction, scalar and vector products, unit vector - One Line Questions
1.
If A = 2i - 5j, what is the unit vector in the direction of A? —
(2i - 5j) / sqrt(29)
2.
If the angle between two vectors A and B is 90 degrees, then A . B = ? —
0
3.
If the angle between two vectors A and B is 0 degrees, then A x B = ? —
0
4.
If A = 5i and B = 2j, what is the magnitude of A x B? —
10
5.
If A = 5i and B = 2i, what is the magnitude of A x B? —
0
6.
If A = 2i + 3j and B = -3i - 2j, what is the scalar product A . B? —
-12
7.
If A = 2i + 3j and B = -3i - 2j, what is the magnitude of A+B? —
1
8.
If two vectors are perpendicular to each other, the angle between them is: —
90 degrees
9.
The angle between vector A = i and vector B = j is: —
90 degrees
10.
The angle between vector A = i and vector B = -i is: —
180 degrees
11.
The vector sum of two vectors A and B is maximum when the angle between them is: —
0 degrees
12.
The vector sum of two vectors A and B is minimum when the angle between them is: —
180 degrees
13.
Let A = 2i + 3j and B = 4i - j. What is A x B? (Assuming 2D vectors in xy-plane, cross product yields a k component) —
-11k
14.
The resultant of two vectors A and B, each of magnitude 'a', acting at an angle 'theta' is given by: —
2a cos(theta/2)
15.
Let A = i + j and B = i - j. What is A + B? —
2i
16.
Let A = i + j and B = i - j. What is A - B? —
2j
17.
If A = 3i + 4j, what is the magnitude of vector A? —
5
18.
Let A = 2i + 3j and B = 4i - j. What is A . B? —
-5
19.
If a vector has components Ax = 5 and Ay = -12, its magnitude is: —
13
20.
If two vectors have magnitudes 3 and 4, and the angle between them is 60 degrees, what is the magnitude of their scalar product? —
6
21.
If two vectors have magnitudes 3 and 4, and the angle between them is 60 degrees, what is the magnitude of their vector product? —
12
22.
A unit vector in the direction of a given vector A is represented by: —
A / |A|
23.
Which of the following is a correct representation of a vector in component form? —
A = Ax i + Ay j
24.
Which of the following represents the zero vector? —
A vector with zero magnitude
25.
The magnitude of a vector can be: —
Zero or positive
26.
The vector product A x B is generally NOT equal to B x A. Instead, A x B =: —
-B x A
27.
Which property is NOT satisfied by the scalar product of two vectors? —
Associative property
28.
Which property is NOT satisfied by the vector product of two vectors? —
Commutative property
29.
The resultant of two forces F1 and F2 acting at an angle theta is given by R. If the angle between F1 and F2 is increased, the magnitude of R will: —
Decrease
30.
The direction of a vector can be indicated by: —
An arrow head
31.
In a 3D Cartesian coordinate system, the unit vectors along the positive x, y, and z axes are respectively: —
i, j, k
32.
A vector quantity is one that possesses: —
Both magnitude and direction
33.
Which of the following is a vector quantity? —
Displacement
34.
The scalar product of two perpendicular vectors is: —
Minimum (zero)
35.
The vector product of two parallel vectors is: —
Minimum (zero)
36.
Which of the following is NOT a vector quantity? —
Work
37.
If two vectors have the same magnitude and direction, they are considered: —
Equal vectors
38.
If A . B = 0 and neither A nor B is a zero vector, then vectors A and B are: —
Perpendicular
39.
If A x B = 0 and neither A nor B is a zero vector, then vectors A and B are: —
Parallel or antiparallel
40.
The direction of the resultant vector of two vectors A and B can be found using: —
Tangent of an angle involving their components
41.
The vector product (cross product) of two vectors A and B is defined as A x B = |A||B|sin(theta)n, where n is a unit vector perpendicular to the plane containing A and B. This product results in a: —
Vector quantity
42.
The angle that a vector A = Ax i + Ay j makes with the positive x-axis is given by: —
tan(theta) = Ay / Ax
43.
The subtraction of two vectors A and B (A - B) is equivalent to: —
The addition of A and -B
44.
A vector can be represented graphically by an arrow, where the length of the arrow represents: —
The magnitude of the vector
45.
The vector product of a vector with itself is: —
Zero vector
46.
When adding two vectors graphically using the head-to-tail method, the resultant vector is drawn from: —
The tail of the first vector to the head of the second vector
47.
The scalar product of two vectors A and B is defined as A . B = |A||B|cos(theta), where theta is the angle between them. This product results in a: —
Scalar quantity
48.
Which of the following is a scalar quantity? —
Speed
49.
The scalar product of a vector with itself is equal to: —
The square of the magnitude of the vector
50.
A unit vector is a vector with: —
Unit magnitude (magnitude of 1)