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