Practise 46 real Federal Board questions on Vectors from 2023 to 2026. See the answer and explanation as soon as you answer.
Vectors is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th and 12th class), and about 10% of its real questions come from it. Tayyari Karo has 46 real questions on this chapter from 2023 to 2026; 21 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 28 medium, 12 easy, 6 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
These are real past-paper questions. Think of your answer first, then open the explanation.
Scalar product of two non-zero vector is maximum when both vectors are:
Answer: A. Parallel
a·b=|a||b|cosθ is maximum (=|a||b|) when θ=0 (parallel, same direction).
For the vector function r(t)=⟨ln(t−1),√(4−t)⟩, the domain in ℝ is:
Answer: C. (1,4]
t−1>0 ⇒ t>1; 4−t≥0 ⇒ t≤4 ⇒ (1,4].
A force F→=2î+ĵ+3k̂ moves an object along a displacement vector d→=3î+4ĵ−2k̂. What is the work done?
Answer: C. 4
W=F→·d→=6+4−6=4.
For what value of x, vectors 2i−j+3k and xi+2j−2k are orthogonal (mutually perpendicular)?
Answer: D. 4
Dot product 2x−2−6=0 ⇒ x=4.
What is the projection of a along b if a = 3i + j − k and b = i?
Answer: A. 3
Projection of a along b = (a·b)/|b| = [(3)(1)+(1)(0)+(−1)(0)] / 1 = 3.
What is the Cosine of the angle that a vector v=√2i+j+k makes with the y‑axis?
Answer: A. 60°
|v|=√(2+1+1)=2. Cos(angle with y‑axis) = (component along j)/|v| = 1/2, so the angle is 60°.
A force F→=3î−2ĵ+k̂ acts at point (1,2,3). Find the moment about the origin.
M→ = r→×F→ where r→=(1,2,3)
= (2(1)−3(−2), −(1(1)−3(3)), 1(−2)−2(3)) = (2+6, −(1−9), −2−6)
M→ = 8î+8ĵ−8k̂
If a→=5î−2ĵ+k̂ and b→=î+2ĵ+2k̂, then find projection of a→ along b→ and projection of b→ along a→.
a→·b→ = 5−4+2 = 3; |b→|=3; |a→|=√30
Projection of a→ along b→ = (a→·b→)/|b→| = 3/3 = 1
Projection of b→ along a→ = (a→·b→)/|a→| = 3/√30 = √30/10 ≈ 0.548
| Session | Questions |
|---|---|
| 2026 Annual | 12 |
| 2025 1st Annual | 10 |
| 2025 2nd Annual | 11 |
| 2024 Annual | 9 |
| 2023 Annual | 4 |
46 real Federal Board (FBISE) Mathematics questions on Vectors from 2023 to 2026, for 11th and 12th class. Each one shows the session it came from.
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
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