Question

What type of physical quantity work is? Scalar or Vector.

Answer 1

Hint: In physics, we talk mainly about two types of quantities: a vector quantity and a scalar quantity. A scalar quantity is one which does not have any direction but only a magnitude. A vector quantity is one which has both direction as well as a magnitude.

Complete step-by-step answer:
We first need to understand what are scalar and vector quantities.
Some physical quantities can be completely described by just their magnitude. Such quantities are known as scalar quantities. These quantities can be added or subtracted from each other by simple rules of algebra. For example: mass of a body, speed of a body, etc.
But there are certain physical quantities which cannot be described by just their magnitude but also require some knowledge of their direction to get their complete knowledge. Such quantities are known as vectors. For example: velocity of a body, acceleration of a body, etc.
Now when we talk about work then it's defined as the product of the force applied on a body and the displacement produced in that body due to the applied force. Mathematically, it is given as
$W = \overrightarrow F .\overrightarrow d $
Work is a scalar quantity because it only has a magnitude and no direction is required to specify it.

Note: It should be noted that work is equal to the scalar product of two vector quantities: force and displacement. The quantity obtained from a scalar product or dot product is always a scalar quantity. Similarly, the quantity obtained from a vector product or a cross product is always a vector quantity. For example: the angular momentum is a vector quantity obtained from the cross product of radial displacement and the linear momentum.
$\overrightarrow L = \overrightarrow r \times \overrightarrow p $