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