Question

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

Answer 1

Hint: All physical quantities are classified into three categories. These categories are scalars, vectors and tensors. The algebraic operations on each one of them differs from the one another. Direction plays a very important role in classifying the physical quantities into these three categories.

Complete solution:
Scalar Quantity:
A quantity which requires only the magnitude in the number field accompanied by the units of measurement or SI units is known as a scalar quantity. Scalar quantities do not require direction to define the physical quantity.
Examples of scalar quantities are: Distance, mass, temperature, energy, work, speed.
Now, that we know that scalar quantities do not require direction we can rule out option (c) to be incorrect.
Vector Quantity:
A quantity which requires both the magnitude in number field along with the direction of the quantity accompanied by the units of measurement or SI units is known as a vector quantity. Vector quantities should also obey the triangular law of vectors.
The triangular law of vectors states that when two vectors are represented as two sides of a triangle with their magnitude and direction taken in account then the resultant of these vectors is represented by the third side of the triangle in the reverse direction.
The direction in the vector quantities are indicated using arrows.
Examples of vector quantities are: displacement, velocity, acceleration, momentum, force.

Tensor Quantity:
A quantity which is defined using an array of functions or numbers which according to the changes of coordinates is known as a tensor quantity. The tensors are defined at every point of space.
Tensor is the most general form of defining a physical quantity and scalars and vectors are also classified under tensors.
Tensors of order zero are called as scalars, tensors of first order are called as vectors and tensors of second order are called as inertial matrices.
Now, from the definitions of the vectors and tensors we know that a quantity which has a direction can be a vector or tensor. For the quantity to definitely be a vector it also needs to follow the triangle law of vectors. Since it is not mentioned in the question whether the quantity follows the triangle law or not, thus the quantity may be a vector or may not be a vector.

Therefore, option (B) is the correct answer.

Note: Vector quantities are further classified into various categories namely: null vector or zero vector, unit vector, position vector, like and unlike vectors, coplanar vectors, collinear vectors, equal vectors. Vectors play an important role in our lives, from finding our location using GPS to targeting enemies in the battlefield or launching satellites, all require use of vectors.