Explain why pressure and surface tension are not vectors?

Hint: A vector must have both magnitude and direction that are defined independently for it irrespective of its application along with other physical quantities. A vector must also follow the vector laws of addition. The direction of surface tension and pressure depends upon the surfaces upon which they act.

Complete step by step answer:
A vector is defined as a physical quantity that has both magnitude and direction and follows the vector laws of addition. The direction and magnitude of the vector must be defined of its own and not depend upon other physical quantities.
Pressure is the component of the force acting on a surface that is perpendicular to the surface per unit surface area. Hence, the magnitude of pressure (component of the force) and its direction depends upon the orientation of the surface. Hence, in essence, it can be said that the direction and magnitude of pressure depends upon the orientation of the surface and is not independent. Also, pressure does not follow the vector laws of addition. Hence, pressure is not a vector quantity.
Surface tension is the force of the surface of a fluid that is perpendicular on both sides to a line on the surface per unit length of the line. Hence, it can be said that the magnitude of the force and its direction is dependent on the orientation of the line that is considered on the surface. Hence, the magnitude and direction of the surface tension is dependent upon the orientation of a line on a surface. Also, surface tension does not follow the vector laws of addition. Hence, surface tension is not a vector quantity.

Note: Surface tension and pressure are in fact tensor quantities of rank zero, which in essence, means that they can be considered as scalar quantities. Similarly, many students also get confused and think that current is a vector quantity, since there is a direction of current. However, students must realize that in a junction, currents are added algebraically and not using vector laws of addition. Students must be aware of this concept as this tricky concept is used in many questions to test students’ understanding.