Which of the following set of quantities have members which are all vectors?

Analyze the question: We need the option in which every quantity has both magnitude and direction (vectors).

Concept:

• Vector: has magnitude and direction (e.g. force, displacement, velocity, acceleration, momentum, weight).
• Scalar: has magnitude only (e.g. distance, speed, mass, energy, work, pressure, density, volume).

Checking each option:

• A. Pressure, energy and force: Pressure is a scalar and energy is a scalar. Only force is a vector. ✗
• B. Force, displacement and momentum: Force is a vector (it acts in a direction). Displacement is a vector (distance in a specified direction). Momentum (mass × velocity) is a vector, with the direction of the velocity. All three are vectors. ✓
• C. Distance, acceleration and work: Distance is a scalar and work is a scalar. Only acceleration is a vector. ✗
• D. Density, volume and weight: Density and volume are scalars. Only weight is a vector. ✗

Answer: Option B is the only set in which every member is a vector.

Tip: Ask yourself, "Do I need to say which way?" If yes, it is a vector. Remember that work, energy, pressure, distance, speed, mass, density and volume are scalars. Do not be confused by pressure: it acts on surfaces, but it is still a scalar. Also, work is force × displacement, but it is a scalar because it comes from a dot product.