Why area is a vector quantity

It is possible that the lines of force crossing the area become zero in some orientation. We can look it up in Gauss divergence theorem. Commoly area is a scalar quantity because there is no need of direction to define and also follow the algebrac summation. When we talk about vector there exist a frame of reference with a certain origin. Dealing with physical quantity, which depends upon area, we have to treat area as vector field which is known as areal vector. Still only area is a scalar. Twings Science Hub.

Er Rajnikant. It is because of the logic that we define things depending on the context. Here, why would you require direction of an area. In this case, area is a vector. Saurabh Raghuvanshi. Nitin Bharti. Sunita Singh. Rajan Mittal. View 12 more Answers. Rameesa B 22 Sep. Dr Bhargavi D. Quality education does not only help children to get a successful career and life, but it also hugely contributes to society.

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We can explain it here but there's no substitute for a full textbook walkthrough. You can't have figured that out by dimensional analysis alone, because this only works in three dimensions: in two dimensions there is no perpendicular direction and in four dimensions there is more than one. In any case, a vector is an element of a vector space. When viewed against the definitions, the real numbers form a vector space, as does the space of polynomials, etc.

The nomenclature of "scalar, vector, tensor" derives from a scheme where tensors are used, and one is seeking the invariants. As it currently stands, your question is quite likely to be closed as a duplicate. Show 4 more comments. Active Oldest Votes. Featured on Meta. Now live: A fully responsive profile. In which case, we can encode the information as a vector, with the magnitude representing the scalar area; the choice as you noticed of pointing out of any given side is exactly that a choice but one that can be made consistently.

We can extend this to non-infinitesimal planes, but it doesn't work that well for curved surfaces. To be precise, what you really want is a co-vector.

This is an abstract gadget which takes a vector and spits out a scalar. Now, we can ask the question of how to represent this abstract co-vector, and it turns out that a vector is a good idea! Specifically, we can represent the action as taking the dot product, which naturally encodes the linearity and the cosine.

Now, in general, this happens to have the same number of dimensions as a proper vector, but this only encodes an area a 2D surface in 3D in 2D you would get a line, in 4D a volume yes! A 4-vector intersects a volume at one point! If you want to learn more about this sort of thing, you want to investigate differential geometry, where all it is necessary to be clear about this sort of thing and not mix up vectors and co-vectors called forms in that field.

A good readable reference is Gauge Fields, Knots and Gravity which starts from a basic overview of the mathematics and develops it for physical use. You know pressure is a scalar there is no direction associated with it , and a force is a vector it acts along an axis. So what does that mean for pressure. The direction of the force is normal to the area, and its magnitude is proportional to the size of the area.

There is an especially picturesque example of the Law of Pythagors in three dimensions applied to the areas of a simplex. Where by "simplex" I believe I mean a section of space bounded by three orthogonal planes and one arbitrary plane. The sum of the squares of the areas of the three small faces are equal to the square of the area of the oblique face. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. How can area be a vector? Ask Question. Asked 10 years, 2 months ago. Active 11 months ago. Viewed 61k times. A Google search gave me the following definition for a vector: Noun: A quantity having direction as well as magnitude, esp. Does considering area as a vector have any real significance? Please explain. Thanks in advance. Improve this question. David 3 3 silver badges 18 18 bronze badges.