A force F = 3ĵ N acts at a point with position vector r = 2î m from the axis. What is the torque?
Correct answer C. 6k̂ N m
Topic / 30 questions
Vectors and Equilibrium MCQs
Vectors and Equilibrium MCQs test how vectors are added using rectangular components and how the scalar (dot) and vector (cross) products depend on the angle between two vectors. They suit MDCAT, ECAT and FSc revision, and every question on MCQs360 shows its correct answer instantly.
- Electromagnetic Induction 30
- Fluid Dynamics 30
- Electrostatics 30
- Electronics 30
- Electromagnetism 30
- Current Electricity 30
- Work and Energy 30
- Waves 30
- Vectors and Equilibrium 30
- Nuclear Physics 30
- Dawn of Modern Physics 30
- Thermodynamics 30
- Rotational and Circular Motion 30
- Atomic Spectra 30
- Alternating Current 30
- Force and Motion 30
For what value of a are the vectors A = 2î + aĵ and B = 3î − 6ĵ perpendicular?
Correct answer C. 1
What is the area of the parallelogram whose adjacent sides are A = 3î m and B = (2î + 4ĵ) m?
Correct answer B. 12 m²
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If A = 4î − 2ĵ and B = −î + 6ĵ, what is the magnitude of A + B?
Correct answer C. 5 units
A force F = (3î + 4ĵ) N displaces a body by d = 5î m. How much work is done?
Correct answer B. 15 J
What is the angle between the vectors A = î + ĵ and B = î?
Correct answer C. 45°
Two vectors of magnitudes 6 units and 5 units make an angle of 30°. What is the magnitude of their vector product?
Correct answer A. 15 units²
Two vectors of magnitudes 5 units and 4 units are inclined at 60°. What is their scalar product?
Correct answer D. 10 units²
If A = 2î + 3ĵ and B = 4î + ĵ, what is A × B?
Correct answer C. −10k̂
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If A = 3î + 4ĵ and B = 2î − ĵ, what is A·B?
Correct answer C. 2
A vector has rectangular components Aₓ = 6 units and Aᵧ = 8 units. What is its magnitude and direction from the x-axis?
Correct answer C. 10 units at 53.1°
A vector has components Aₓ = −3 units and Aᵧ = +3 units. What angle does it make with the positive x-axis?
Correct answer C. 135°
A force of 20 N acts at 30° above the positive x-axis. What is its x-component?
Correct answer D. 17.3 N
What is the projection (component) of vector A along the direction of vector B?
Correct answer D. A·B / B
Three coplanar forces keep a body in equilibrium. Which statement about them is correct?
Correct answer A. Any one force is equal and opposite to the resultant of the other two
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Two forces of 3 N and 4 N act at a point. Which of these cannot be the magnitude of their resultant?
Correct answer C. 8 N
For two vectors, |A × B| = A·B. What is the angle between them?
Correct answer A. 45°
The scalar product A·B of two non-zero vectors is negative. What can be said about the angle θ between them?
Correct answer D. 90° < θ ≤ 180°
The magnitude of A × B is geometrically equal to the area of ____
Correct answer C. the parallelogram with A and B as adjacent sides
What is the value of ĵ × î?
Correct answer D. −k̂
About Vectors and Equilibrium MCQs
Questions in this unit ask you to resolve vectors into rectangular components, add them, and find the magnitude and direction of the resultant using unit vectors î, ĵ and k̂. A large share focus on the scalar product: finding A·B from components or from magnitudes and the angle, deciding the angle when the product is zero or negative, and recognising work and power as dot products. Others cover the vector product, its direction by the right-hand rule, and quantities such as torque that are cross products, along with the conditions of equilibrium.
Key facts to remember
- Scalar product: A·B = AB cos θ = AₓBₓ + A_yB_y + A_zB_z; it is commutative.
- Vector product: |A × B| = AB sin θ, and A × B = −(B × A), so it is anti-commutative.
- Resultant from components: R = √(Rₓ² + R_y²), with direction θ = tan⁻¹(R_y/Rₓ).
- Unit vectors: î·î = 1, î·ĵ = 0, î × ĵ = k̂ and î × î = 0.
- Work W = F·d is a scalar product, while torque τ = r × F is a vector product.
- A body is in complete equilibrium when ΣF = 0 (first condition) and Στ = 0 (second condition).
Exams that include Vectors and Equilibrium MCQs
Pakistan
- MDCAT
- ECAT (UET)
- NUMS
- AKU
- FSc boards
India
- NEET
- JEE Main
Bangladesh
- HSC
- Medical Admission Test
How to prepare for Vectors and Equilibrium MCQs
- Remember that A·B = 0 means the vectors are perpendicular, and a negative A·B means the angle is between 90° and 180°.
- When vectors are given in î, ĵ form, multiply matching components for the dot product rather than finding the angle first.
- Make a short list of physical quantities that are dot products (work, power, flux) and cross products (torque, angular momentum, magnetic force).
- Practise the right-hand rule on a few examples so you can find the direction of a cross product quickly.
Frequently asked questions
Which exams ask Vectors and Equilibrium MCQs?
Vectors and Equilibrium is part of the FSc physics syllabus, so its MCQs appear in MDCAT, ECAT (UET), NUMS and AKU entry tests and in FSc board papers. Students in India meet the same ideas in NEET and JEE Main, and Bangladeshi students in HSC and the medical admission test.
What is the difference between the dot and cross product?
The dot product A·B = AB cos θ gives a scalar and is largest when the vectors are parallel. The cross product has magnitude AB sin θ, gives a vector perpendicular to both, and is largest when they are at 90°. Work is a dot product and torque a cross product.
Last reviewed October 2026