Sign In

Mathematics for IGCSE & O level - Vectors (Section 4)

1
If vector v = [3, 0], then what is its horizontal component?
Answer
(B)
3
2
Which describes the vector that would move a point from (1, 3) to (5, 1)?
Answer
(C)
[4, -2]
3
In a triangle ABC, if AB = a and AC = 2a, what is the vector BC?
Answer
(A)
a
4
Which of the following statements is correct regarding a scalar multiple of a vector?
Answer
(C)
A scalar multiple only changes the magnitude, not the direction (unless the scalar is negative).
5
If |v| = 5, which of the following is true?
Answer
A
C
D
6
If vector a = [2, 5], what is the magnitude of -a?
Answer
(B)
√29
7
Which statement best describes the addition of vectors a and b?
Answer
B
D
8
What vector results when the components of vector [2, -4] are multiplied by -1?
Answer
(A)
[-2, 4]
9
What is the magnitude of a vector with components (-8, 6)?
Answer
(B)
10
10
If vector a = [4, -2], what is 0 * a?
Answer
(B)
[0, 0]
11
A transformation that moves points in a given direction for a given distance is called a ______.
Answer
(B)
Translation
12
Which of the following best describes the effect of a negative scalar on a vector?
Answer
A
D
13
Given that OA = a and OB = b and M is the midpoint of AB. What vector represents OM?
Answer
(C)
1/2(a + b)
14
If vector v = [x, y], which formula represents the magnitude of v?
Answer
(C)
√(x^2 + y^2)
15
Which operations can be performed on vectors?
Answer
A
B
C
16
Given a vector a, the result of 3a is that the vector is _____.
Answer
(A)
Multiplied by 3
17
What does vector addition represent geometrically?
Answer
(C)
Combining displacements
18
If a vector is represented by [a, b], then which component dictates vertical movement?
Answer
(B)
b
19
Which of the following describes vector subtraction geometrically?
Answer
(A)
Adding a vector's negative.
20
What is meant by a scalar?
Answer
(B)
A quantity that has magnitude
21
If vector a = [x, y], what represents the direction of the vector a?
Answer
(C)
arctan(y/x)
22
If the vector from A to B is denoted by AB, and the vector from B to C is denoted by BC, then which expression represents the vector from A to C?
Answer
(C)
AB + BC
23
Given the vector v = [4, -3], what is its magnitude?
Answer
(A)
5
24
If OA = a, OB = b, and the point C is such that OC = a + b, what is the geometrical shape of OACB?
Answer
(C)
A parallelogram
25
What does the term 'scalar' refer to in vector context?
Answer
(C)
A number that multiplies a vector
26
What geometrical concept is described by a vector?
Answer
(D)
All of the above
27
A vector can be described by its:
Answer
A
B
28
Which of the following operations are valid operations with two vectors?
Answer
A
B
29
If AB = [4, -1] and CD = [8, -2], what can we say about their relationship?
Answer
(B)
AB and CD have the same direction
30
If vector p = [6, -8], what is the magnitude of vector p?
Answer
(B)
10
31
What are column vectors also commonly used to represent?
Answer
(B)
Displacements
32
What geometric shape is often used to visualize the addition of two vectors?
Answer
(D)
Parallelogram
33
Which of the following is NOT a property of a vector?
Answer
(D)
Color
34
If a and b are position vectors and a + b = c, which statement best describes the relationship?
Answer
(B)
c represents the sum of the vectors a and b.
35
The vector notation [2, -3] is also known as a:
Answer
(C)
Column vector
36
If vector v = [x, y], which expression correctly describes the calculation of the magnitude of v?
Answer
(C)
√(x^2 + y^2)
37
Which transformation is described by the vector [a, b]?
Answer
(C)
Translation
38
What does the term 'magnitude' refer to in the context of a vector?
Answer
(B)
The length/size of the vector
39
If a translation moves a point 3 units to the left and 4 units up, what is the translation vector?
Answer
(B)
[-3, 4]
40
If a vector has a magnitude of 0, what can you conclude?
Answer
(D)
All of the above.
41
How is vector subtraction performed?
Answer
(A)
Subtracting the corresponding components
42
Which vector represents a translation of 3 units to the right and 1 unit down?
Answer
(D)
[3, -1]
43
If a translation is represented by the vector [-2, 3], the point is moved:
Answer
(C)
2 units left and 3 units up
44
If a and b are two non-zero vectors and |a + b| = |a| + |b|, what does this imply about the relationship between vectors a and b?
Answer
(B)
a and b are parallel and in the same direction
45
If vector a is [1, 2] and b is [-1, 0], which is a - 3b?
Answer
(A)
[4, 2]
46
Given a = [1, 0] and b = [0, 1], what can you say about vectors a and b?
Answer
(B)
They are perpendicular.
47
Given vectors a and b, if a = [1, 2] and b = [3, -1], what is a + b?
Answer
(A)
[4, 1]
48
If A is the point (1, 2) and B is the point (4, 6), then the vector AB is:
Answer
(A)
[3, 4]
49
What kind of quantity is a vector?
Answer
(C)
A quantity that has both magnitude and direction
50
What is the column vector that represents a translation that maps point (2, 1) to (5, 4)?
Answer
(A)
[3, 3]