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