A physical quantity which has a direction:

A) Must be a vector

B) May be a vector

C) Must be a scalar

D) Must be zero

Scalar Quantity

A scalar quantity is defined as a physical quantity that requires only magnitude (numerical value) along with the appropriate unit of measurement (SI unit). Scalars do not require direction for their definition.

Examples: Distance, mass, temperature, energy, work, speed.

Since scalars lack direction, we can rule out option (C) as incorrect.

Vector Quantity

A vector quantity requires both magnitude and direction, along with units of measurement. Vectors must also obey the triangle law of vector addition.

• Triangle law of vectors: If two vectors are represented as two sides of a triangle (considering both magnitude and direction), the resultant vector is given by the third side of the triangle, taken in the opposite direction.
• The direction of a vector is usually shown using arrows.

Examples: Displacement, velocity, acceleration, momentum, force.

Tensor Quantity

A tensor quantity is defined using an array of numbers or functions that transform according to changes in coordinates. Tensors are defined at every point in space and represent the most general form of physical quantities.

• Scalars are tensors of order zero.
• Vectors are tensors of first order.
• Second-order tensors include quantities like inertial matrices.

Thus, any quantity with direction can be either a vector or a tensor. However, for it to be classified specifically as a vector, it must obey the triangle law of vectors. Since the question does not specify whether this law is followed, the given quantity may or may not be a vector.

Final Answer

Therefore, option (B) is the correct answer.