Vectors Practice Questions
HSC/SSC (Bangladesh) · HSC Mathematics · 146 free MCQs with instant results and detailed explanations.
146
Total
50
Easy
75
Medium
21
Hard
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Sample Questions from Vectors
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Q1
Easy
Which of the following represents a vector quantity?
A.
5 m/s (speed)
B.
10 N (force)
C.
30ยฐC (temperature)
D.
15 kg (mass)
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Correct Answer: B
Force is a vector quantity because it has both magnitude (10 N) and direction. The other options represent scalar quantities.
Q2
Easy
If vector A = 3i + 4j and vector B = -2i + j, what is vector A + vector B?
A.
i + 5j
B.
i + 3j
C.
5i + 5j
D.
1i + 5j
Show Answer & Explanation
Correct Answer: D
Adding the vectors results in (3i - 2i) + (4j + j) = (3 - 2)i + (4 + 1)j = 1i + 5j.
Q3
Easy
A vector is said to be a unit vector if its magnitude is equal to:
A.
0
B.
1
C.
2
D.
Any positive number
Show Answer & Explanation
Correct Answer: B
A unit vector has a magnitude of exactly 1, making option B the correct choice. Other options do not describe the properties of a unit vector.
Q4
Medium
A vector C is given by C = 4i + 3j. What is the magnitude of vector C?
A.
5
B.
7
C.
10
D.
25
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Correct Answer: A
The magnitude of vector C is calculated using the formula |C| = โ(Cxยฒ + Cyยฒ). Here, |C| = โ(4ยฒ + 3ยฒ) = โ(16 + 9) = โ25 = 5.
Q5
Medium
If vector D = 5i + 12j and vector E = -3i + 4j, what is the resultant vector R = D + E?
A.
2i + 16j
B.
2i + 8j
C.
8i + 16j
D.
8i + 8j
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Correct Answer: A
The resultant vector R is found by adding corresponding components: R = (5 - 3)i + (12 + 4)j = 2i + 16j.
Q6
Medium
Given vectors G = i + 2j and H = 3i - 4j, what is the angle ฮธ between vectors G and H?
A.
60 degrees
B.
45 degrees
C.
30 degrees
D.
90 degrees
Show Answer & Explanation
Correct Answer: B
The angle ฮธ can be calculated using the formula cos(ฮธ) = (G ยท H) / (|G| * |H|). Here, the dot product G ยท H = 1*3 + 2*(-4) = -5, and the magnitudes |G| = โ5 and |H| = โ(9 + 16) = 5, giving cos(ฮธ) = -5 / (โ5 * 5). Thus, ฮธ = 45 degrees.
Q7
Medium
Which of the following statements is true about two non-zero vectors A and B if A + B = 0?
A.
A and B are equal in magnitude and opposite in direction.
B.
A and B are equal in magnitude and direction.
C.
A and B are perpendicular to each other.
D.
A and B have different magnitudes.
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Correct Answer: A
If A + B = 0, it implies that vector A must cancel out vector B; hence, they must be equal in magnitude but opposite in direction.
Q8
Hard
If vectors A = (3, -2, 1) and B = (k, 4, -5) are orthogonal, what is the value of k?
A.
2
B.
3
C.
4
D.
5
Show Answer & Explanation
Correct Answer: A
Two vectors are orthogonal when their dot product is zero. So, (3 * k) + (-2 * 4) + (1 * -5) = 0 leads to 3k - 8 - 5 = 0, thus 3k = 13, and k = 2.
Q9
Hard
A vector **C** is defined as **C** = **A** + **B**, where **A** = 2i + 3j and **B** = -i + 4j. What is the magnitude of vector **C**?
A.
5
B.
7
C.
โ29
D.
โ25
Show Answer & Explanation
Correct Answer: C
To find the magnitude of **C**, first calculate **C** = (2 - 1)i + (3 + 4)j = i + 7j. The magnitude is โ(1^2 + 7^2) = โ(1 + 49) = โ50.
Q10
Hard
If vector A = 3i + 4j and vector B = 2i - j, what is the angle between the two vectors?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show Answer & Explanation
Correct Answer: C
The angle between vectors A and B can be found using the dot product formula. The cosine of the angle ฮธ is given by the formula: cos(ฮธ) = (A ยท B) / (|A| |B|). After calculating, we find that ฮธ is 60 degrees.
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Vectors โ HSC/SSC (Bangladesh) HSC Mathematics Practice Questions Online
This page contains 146 practice MCQs for the chapter Vectors in HSC/SSC (Bangladesh) HSC Mathematics. The questions are organized by difficulty โ 50 easy, 75 medium, 21 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.