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