Mathematics for IGCSE & O level - Vectors (Section 3)
1
Given points A(1, 2) and B(4, 6), what is the column vector AB?
Хариулт
(B)
[3, 4]
2
If vector p = 3i + 4j, what is the magnitude of p?
Хариулт
(C)
5
3
Given points A(1, 1) and B(4, 5). What is the magnitude of the vector AB?
Хариулт
(B)
5
4
The vector AB has an x coordinate increase of 2 and y coordinate increase of -3, which vector represents that change?
Хариулт
(D)
[2, -3]
5
Which of the following vector operations are valid?
Хариулт
A
B
6
What does the vector describe?
Хариулт
(D)
The change in x and y coordinates
7
Given a vector a = [1,2], what is the vector -a?
Хариулт
(C)
[-1, -2]
8
Given vector a = [3, 1] and b = [-1, 2], what is the result of a - b?
Хариулт
(D)
[2, 3]
9
What is the vector that results when a vector is multiplied by -1?
Хариулт
(B)
A vector with the same magnitude but opposite direction
10
Which is the correct vector equation for finding the displacement of point P after translation with vector v?
Хариулт
(A)
P + v
11
If point P(2, 3) is translated using the vector [-1, 4], what are the coordinates of P'?
Хариулт
(A)
(1, 7)
12
If vector AB = 2*vector CD, what is the relationship between the vectors?
Хариулт
(B)
AB is twice as long as CD
13
What is the term for a vector's size?
Хариулт
(A)
Magnitude
14
Given a vector AB, and a point M as the midpoint of AB, which equation is correct?
Хариулт
(A)
AM = MB
15
If the position vectors of points A and B are given by a and b respectively, which expression correctly represents the vector AB?
Хариулт
(B)
b - a
16
Given that the point A has position vector a and B has position vector b, what expression gives the position vector of the midpoint M of AB?
Хариулт
(C)
1/2(a+b)
17
In a triangle ABC, if AB = a and BC = b, what does AC represent?
Хариулт
(C)
a + b
18
Given a vector, how do you find its negative?
Хариулт
(D)
a & c are correct
19
If a = [2, 1] and b = [-1, 3], what is the result of a - 2b?
Хариулт
(D)
[4, 7]
20
In the parallelogram rule, given vectors a and b, what represents the diagonal?
Хариулт
(C)
a + b
21
If AB is parallel to CD and twice the length of CD, which of the following statements is true?
Хариулт
A
D
22
If A = (2, 3) and B = (5, 7), what is the vector AB?
Хариулт
(C)
[3, 4]
23
What does the expression AB - AC represent?
Хариулт
(B)
BC
24
If a = [2, 3], and b = [-1, 2], then a + 2b = ?
Хариулт
(A)
[0, 7]
25
What is the effect of multiplying a vector by a scalar?
Хариулт
(B)
It changes the magnitude of the vector.
26
What is the resultant vector of a + b, given a = [1, 2] and b = [3, 4]?
Хариулт
(A)
[4, 6]
27
Given that vector p = [2, 1] and vector q = [3, -1], what is the result of 2p - q?
Хариулт
(A)
[1, 3]
28
If two vectors are equal, what can be said about their magnitude and direction?
Хариулт
(B)
Equal magnitudes and the same direction
29
If a vector a = [2, 3], what does -2a represent?
Хариулт
(C)
A vector twice as long as a, but in the opposite direction.
30
A negative value in the top number of a column vector indicates movement ______. A negative value in the bottom number of a column vector indicates movement ______.
Хариулт
(A)
left, down
31
Which component of a vector describes its orientation?
Хариулт
(B)
Direction
32
What transformation does the vector [-1, 0] represent?
Хариулт
(B)
A translation 1 unit left
33
Which of the following is NOT a component of a vector?
Хариулт
(C)
Origin
34
If the position vector of P is p and the position vector of Q is q, then what vector equals PQ?
Хариулт
(C)
q - p
35
What does the term 'collinear' mean in the context of vectors?
Хариулт
(B)
The vectors are parallel and lie on the same line.
36
What is the relationship between the position vector of a point and the coordinates of the point?
Хариулт
(B)
The position vector's components are the same as the point's coordinates.
37
If the vector [2, -1] represents a translation, which describes the move?
Хариулт
(B)
2 units right, 1 unit down
38
If vector a = [2, 4] and b = [1, -3], calculate 2a - 3b.
Хариулт
(B)
[1, 7]
39
If a = [2, 1] and b = [1, 3], what is the magnitude of a + b?
Хариулт
(B)
√13
40
If vector AB = [5, -2] and vector BC = [-1, 3], find vector AC.
Хариулт
(A)
[4, 1]
41
The position vectors of A and B are a = [1, 2] and b = [4, 6] respectively. Find vector AB.
Хариулт
(C)
[3, 4]
42
In a triangle, the vector from A to B is represented by a, and the vector from B to C is represented by b. How is the vector from A to C represented?
Хариулт
(C)
a + b
43
What is the resultant of vector addition also sometimes called?
Хариулт
(B)
Sum
44
In the formula a + b = c, how is the vector c obtained geometrically?
Хариулт
(A)
By placing vector b head-to-tail to a
45
Given the vectors a=[2, 1] and b=[3, -2], what is 2a - b?
Хариулт
(A)
[1, 4]
46
If vector a = [3, 4], what is the magnitude of a?
Хариулт
(C)
5
47
What would be the resulting vector if a vector [3, 4] is multiplied by -2?
Хариулт
(B)
[-6, -8]
48
What is the vector that has both magnitude and direction but no length?
