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