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