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