Mathematics for IGCSE & O level - Vectors (Section 5)
1
Given vector v = [x, y], which statement is correct?
2
A vector's direction is best described by:
3
In the context of vector geometry, what does the term 'parallel' mean regarding two vectors?
উত্তর(C)
The vectors lie in the same plane and never intersect.
4
If a translation moves a point from (1, 2) to (4, 6), what is the translation vector?
5
The magnitude of the vector [3, 4] is:
6
In the context of vectors, which of the following are correct?
7
Which of the following is true about finding the magnitude of a vector?
উত্তর(D)
The magnitude is found by squaring both components and then taking the square root of their sum
8
When a vector is multiplied by a scalar, what aspect(s) of the vector change(s)?
9
Which of the following are true concerning vectors?
10
If vector a = [2,3], and vector b = [4,1], what is the vector 3a + 2b?
11
If A is the point (3, -1) and B is the point (0, 2), what is the magnitude of vector AB?
12
If a translation is described by the vector [-2, 1], what operation is performed on the x and y coordinates?
উত্তর(A)
Subtract 2 from x, add 1 to y.
13
Which operation changes only the magnitude of a vector and not its direction?
উত্তর(B)
Scalar multiplication with a positive scalar
14
Given vector a = [3, -1] and vector b = [-2, 2], then -a + b is:
15
In a parallelogram ABCD, if AB = a and AD = b, then AC equals:
16
Which of the following is equivalent to the vector -v?
17
How is the vector AB defined in terms of position vectors?
18
What type of transformation is described by the vector [0, 4]?
19
If vector a = [2, 0] and b = [0, 3], then 2a + b is:
20
Which of the following are characteristics of a vector?
21
If AB = CD and CD = EF, what is the relationship between AB and EF?
22
Given vector u = [2, -1], and vector v = [-1, 3], what is the result of u + v?
23
Given the vectors a = [1, 0] and b = [0, 1], what is the magnitude of a + b?
24
What is the result when you add the vectors [2, 3] and [-1, 1]?
25
If a is a vector and k is a scalar, what is the effect of multiplying the vector a by the scalar k?
26
What does a position vector in the context of vectors describe?
উত্তর(B)
The position of a point relative to the origin
27
Which geometric transformation is represented by a vector?
28
Which is the result of a - a, where a is a vector?
29
If point A is at (1, 2) and it is translated by the vector [2, 3], what are the new coordinates of A?
30
If AB = [2, 5] and AC = [1, 1], then BC is equal to:
31
Given vector a = [3, -2], which of the following vectors is equal to -2a?
32
The top number in a column vector tells you how the shape moves ______, or in the y-direction.
33
What geometric shape can represent the vector sum of three vectors, where the endpoint of one vector is the start point of the next?
34
In the column vector, [3, -1], the shape moves ______, and ______.
উত্তর(B)
3 units right, 1 unit down
35
Which of the following statements correctly defines a unit vector?
উত্তর(B)
A vector with a magnitude of 1 and a defined direction.
36
If you translate a point with coordinates (x, y) using the vector [a, b], what are the new coordinates of the point?
37
If vector AB = [6, 8], what is the magnitude of the vector -AB?
38
Which of the following represents the zero vector?
39
If a vector 'v' is [2, 3], which is the result of -1/2 v?
40
Given points A(1, 2) and B(4, 6), what is the vector from A to B in component form?
41
Which statement is true about vectors?
42
What geometric figure does the addition of two vectors, represented by the sides, define?
43
In column vector notation, which component indicates the horizontal direction and magnitude of movement?
44
When adding two column vectors, you _______ the corresponding components.
45
Given vector a = [5, 12], what is its magnitude?
46
উত্তর(C)
A vector with a magnitude of 0 and no direction.
47
If vector a = [4, 3], then what is the unit vector of a?
48
Which of the following statements are true regarding vector geometry?
49
If vector a = [5, -1] and vector b = [-2, 3], which of these represents the resultant vector of a + b?
