Vectors Practice Questions
NECO (Nigeria) · NECO Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
51
Easy
67
Medium
27
Hard
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Sample Questions from Vectors
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Q1
Easy
What is the resultant vector of two vectors A = 3i + 4j and B = 1i + 2j?
A.
4i + 6j
B.
2i + 2j
C.
3i + 2j
D.
5i + 6j
Show Answer & Explanation
Correct Answer: A
The resultant vector R = A + B = (3i + 4j) + (1i + 2j) = (3 + 1)i + (4 + 2)j = 4i + 6j.
Q2
Easy
If vector A = 3i + 4j and vector B = 1i + 2j, what is the resultant vector A + B?
A.
4i + 6j
B.
2i + 3j
C.
3i + 2j
D.
5i + 4j
Show Answer & Explanation
Correct Answer: A
The resultant vector A + B is obtained by adding the corresponding components: (3i + 1i) + (4j + 2j) = 4i + 6j.
Q3
Easy
A vector C is defined as C = 5i - 3j. What is the magnitude of vector C?
A.
โ34
B.
โ26
C.
โ15
D.
โ29
Show Answer & Explanation
Correct Answer: A
The magnitude of vector C is calculated using the formula โ(x^2 + y^2). Here, โ(5^2 + (-3)^2) = โ(25 + 9) = โ34.
Q4
Medium
What is the magnitude of the vector C = 6i - 8j?
A.
10
B.
14
C.
8
D.
6
Show Answer & Explanation
Correct Answer: A
The magnitude of a vector C = ai + bj is calculated using the formula โ(aยฒ + bยฒ). Here, โ(6ยฒ + (-8)ยฒ) = โ(36 + 64) = โ100 = 10.
Q5
Medium
If vector A = 4i + 3j and vector B = 2i + 5j, what is the angle ฮธ between the two vectors?
A.
37 degrees
B.
53 degrees
C.
90 degrees
D.
45 degrees
Show Answer & Explanation
Correct Answer: B
The angle ฮธ can be found using the dot product formula: AยทB = |A||B|cos(ฮธ). Here, the angle calculated using vectors A and B gives approximately 53 degrees.
Q6
Medium
Two vectors A and B are given as A = 2i + 3j and B = 4i - k. What is A + B?
A.
6i + 3j - k
B.
2i + 3j + 4k
C.
2i + 7j - k
D.
6i + 3j + k
Show Answer & Explanation
Correct Answer: A
When adding vectors, simply add the corresponding components. Here, A + B = (2 + 4)i + (3 + 0)j + (0 - 1)k = 6i + 3j - k.
Q7
Medium
If the vector P = 5i + 12j represents a point, what is the unit vector in the direction of P?
A.
5/13 i + 12/13 j
B.
5/12 i + 12/5 j
C.
1/13 i + 12/13 j
D.
5/13 i - 12/13 j
Show Answer & Explanation
Correct Answer: A
The unit vector is found by dividing the vector by its magnitude. First, find the magnitude of P: โ(5ยฒ + 12ยฒ) = 13, then the unit vector is (5/13)i + (12/13)j.
Q8
Hard
A vector A has a magnitude of 10 units and is directed at an angle of 30 degrees from the positive x-axis. What are the x and y components of vector A?
A.
(5โ3, 5)
B.
(10, 0)
C.
(8.66, 5)
D.
(3.46, 8.66)
Show Answer & Explanation
Correct Answer: C
The x-component is calculated as 10 * cos(30ยฐ) = 10 * (โ3/2) = 8.66 units, and the y-component is 10 * sin(30ยฐ) = 10 * (1/2) = 5 units. Hence, the correct components are (8.66, 5).
Q9
Hard
A vector A has a magnitude of 10 units and is directed 60 degrees above the positive x-axis. What are the components of vector A?
A.
(5, 5โ3)
B.
(10โ3, 10)
C.
(10, 0)
D.
(5โ3, 5)
Show Answer & Explanation
Correct Answer: D
Using trigonometric functions, the x-component is A*cos(60ยฐ) = 10 * 0.5 = 5 and the y-component is A*sin(60ยฐ) = 10 * (โ3/2) = 5โ3. Thus, the correct components are (5โ3, 5).
Q10
Hard
Two vectors B = (3, -4) and C = (-1, 2) are given. What is the resultant vector R = B + C?
A.
(2, -2)
B.
(4, -6)
C.
(2, 6)
D.
(1, -2)
Show Answer & Explanation
Correct Answer: A
To find the resultant vector R, add the corresponding components of vectors B and C: R = (3 + (-1), -4 + 2) = (2, -2). Therefore, the correct answer is (2, -2).
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Vectors โ NECO (Nigeria) NECO Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Vectors in NECO (Nigeria) NECO Mathematics. The questions are organized by difficulty โ 51 easy, 67 medium, 27 hard โ so you can choose the right level for your preparation.
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