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Mathematics for IGCSE & O level - Vectors (Section 6)

1
If AB = [3, -1], what is the vector BA?
Answer
(B)
[-3, 1]
2
If vector 'a' is [2, 1] and a is multiplied by a scalar 3, what is the result?
Answer
(A)
[6, 3]
3
If a force is represented by a vector, what aspects does the vector specify about the force?
Answer
A
C
4
Which is a characteristic of a parallelogram, given vectors?
Answer
A
C
D
5
If a translation is defined by the vector [2, -3], how does it affect the x and y coordinates of a point?
Answer
(A)
Adds 2 to the x-coordinate and subtracts 3 from the y-coordinate.
6
Which of the following transformations can be represented by a vector?
Answer
(C)
Translation
7
Which is true if AB = -CD?
Answer
(C)
AB is in the opposite direction as CD and has the same length.
8
If vector a = [1, 4] and vector b = [2, -1], what is a - b?
Answer
(C)
[-1, 3]
9
A vector that starts at the origin is often referred to as a ______ vector.
Answer
(B)
Position
10
In a triangle with vertices A, B, and C, and given AB = a and BC = b, which of the following expresses the vector AC?
Answer
(C)
a + b
11
Which of the following statements about vector AB is true?
Answer
(A)
It has both magnitude and direction.
12
How do you find the column vector that represents the movement from (x1, y1) to (x2, y2)?
Answer
(A)
Subtract (x1, y1) from (x2, y2)
13
What is the geometric interpretation of -v, given a vector v?
Answer
(A)
A vector with the same magnitude but opposite direction.
14
If vector v = [-3, -4], what is the magnitude of v?
Answer
(B)
5
15
Given vector a = [x, y], and scalar k, which of the following statements are true regarding ka?
Answer
A
C
16
If a = [1, -1] and b = [2, 3], what is a - b?
Answer
(A)
[-1, -4]
17
In a coordinate plane, a vector is defined by its _____.
Answer
(D)
All of the above
18
Which of the following is a correct representation of vector PQ?
Answer
(A)
PQ
19
The x-component of the vector [5, -3] is _____ and the y-component is ____.
Answer
(C)
5, -3
20
If vector a = [x, y], what is -1 * a?
Answer
(B)
[-x, -y]
21
Which of these is the correct way to represent vector AB?
Answer
(B)
AB
22
In a parallelogram, what is the relationship between the vectors representing opposite sides?
Answer
(B)
They are equal in magnitude and in the same direction.
23
When are two vectors considered equal?
Answer
(C)
When they have the same magnitude and the same direction.
24
What type of vector is used to describe a position of a point relative to a reference point?
Answer
(A)
Position vector
25
If A is the point (1, 0) and B is the point (0, 1), what is the magnitude of the vector AB?
Answer
(B)
√2
26
If a = [1, 2] and b = [3, 4], what is 2a + b?
Answer
(C)
[5, 6]
27
If vector a = [2, 3] and scalar k = 2, what is ka?
Answer
(A)
[4, 6]
28
Which of the following is true regarding two vectors that are parallel?
Answer
C
D
29
What does the vector [3, -2] mean in terms of movement in a coordinate plane?
Answer
(C)
Move 3 units right, 2 units down.