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