ĵ.(î×k̂) =
- 0
- −1
- 1
- 2
Show answer and explanation
Answer: B. −1
î×k̂ = −ĵ (from the cyclic rule î×ĵ=k̂, ĵ×k̂=î, k̂×î=ĵ). So ĵ.(î×k̂) = ĵ.(−ĵ) = −1.
FSC Physics: Vectors and Equilibrium, questions with answers
Practise 18 real Federal Board questions on Vectors and Equilibrium from 2023 to 2026. See the answer and explanation as soon as you answer.
18real questions
6multiple choice
5exam sessions
About Vectors and Equilibrium in FSC Physics
Vectors and Equilibrium is one of the 14 main chapters in our Federal Board FSC Physics question bank (11th class), and about 4% of its real questions come from it. Tayyari Karo has 18 real questions on this chapter from 2023 to 2026; 6 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 14 medium, 4 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
Torque τ on a body is given by:
- t̄ = m̄ × ā
- t̄ = F̄ × d̄
- t̄ = r̄ × F̄
- t̄ = r̄ × ω̄
Show answer and explanation
Answer: C. t̄ = r̄ × F̄
Torque is the cross product of the position vector and the applied force, τ = r × F.
If the magnitude of A.B = (1/2)AB, then angle between A and B is:
- 60°
- 90°
- 30°
- 45°
Show answer and explanation
Answer: A. 60°
A·B = AB cosθ = (1/2)AB ⇒ cosθ = 1/2 ⇒ θ = 60°.
If Ax = −2, Ay = −2 then resultant vector will make angle:
- 180°
- 225°
- 45°
- 90°
Show answer and explanation
Answer: B. 225°
Both components negative places the vector in the third quadrant: θ = 180° + 45° = 225° (since tan⁻¹(2/2)=45° from the negative x-axis).
Torque τ is defined as the vector product of position vector r (moment arm) and force F. What will be the scalar product of torque τ and position vector r (moment arm)?
- r.r tanθ
- Zero
- r.r sinθ
- r.r cosθ
Show answer and explanation
Answer: B. Zero
τ = r × F is always perpendicular to r, so the dot product τ·r = 0.
Which one of the following is the unit vector of a vector A = 4i − 2j?
- (4/√20)i − (2/√20)j
- (4/√3)i − (2/√3)j
- (4/13)i − (2/13)j
- (4/2√3)i − (2/2√3)j
Show answer and explanation
Answer: A. (4/√20)i − (2/√20)j
|A| = √(4² + 2²) = √20, so the unit vector is A/|A| = (4/√20)i − (2/√20)j.
Describe any three properties of cross product of two vectors.
Show model answer
1. The cross product of two vectors Ā and B̄ is itself a vector, Ā×B̄ = AB sinθ n̂, where n̂ is a unit vector perpendicular to the plane containing Ā and B̄ (direction given by the right-hand rule).
2. It is not commutative: Ā×B̄ = −(B̄×Ā) (reversing the order reverses the direction of the result).
3. The cross product of two parallel (or anti-parallel) vectors is zero, since sinθ = sin0° = 0; it is maximum when the vectors are perpendicular (θ=90°).
State the characteristics of vector (cross) product.
Show model answer
(1) The magnitude is |A×B| = AB sinθ.
(2) The direction is perpendicular to the plane containing A and B, given by the right-hand rule.
(3) It is not commutative: A×B = −(B×A).
(4) It is distributive over vector addition: A×(B+C) = A×B + A×C.
(5) The cross product of a vector with itself is zero: A×A = 0.
(6) It is generally not associative: A×(B×C) ≠ (A×B)×C.
Sessions with Vectors and Equilibrium questions
| Session | Questions |
|---|---|
| 2026 Annual | 3 |
| 2025 1st Annual | 3 |
| 2025 2nd Annual | 2 |
| 2024 Annual | 5 |
| 2023 Annual | 5 |
Common questions
What does the Vectors and Equilibrium chapter cover on this page?
18 real Federal Board (FBISE) Physics questions on Vectors and Equilibrium from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
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.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.