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Three Dimensional Geometry (part - 2) , The Planes | study material for IIT JEE | concept booster, chapter highlights/

THREE DIMENSIONAL GEOMETRY (PART - 2), THE PLANES










THE PLANESPlane is the surface such that if any two points are taken on it, then the line joining the two points lies on it.
General equation of plane is given as -  ax + by + cz + d = 0 , where a ,b and c is not equal to zero.
           POINTS TO BE REMEMBERED 1). a, b and c are the directions ratios of the normal to the plane ax + by + cz + d = 0.

2). Equation of the yz - plane is x = 0

3). Equation of the zx - plane is y = 0

 4). Equation of the xy - plane is z = 0

5). Equation of the any plane parallel to the xy - plane is z = c. Similarly for Planes parallel to yz and zx is x = c and y = c
EQUATION OF THE PLANE IN NORMAL FORMVECTOR FORMIf n̂ be a unit vector normal to a given plane and d be the length of the perpendicular from the origin to the plane, then the equation of the plane is given by -                           r.n̂ = d CARTESIAN FORMIf l, m, n are the directions cosines of the normal to the plane and d is the perpendicular distan…

Mass - Energy Equivalence, (E = mc^2), understanding the basic concepts and it's derivation

Today we are going to talk about a famous formula , which has changed the thinking of the world and who give the underlying concept of time travel. We are talking about the mass - energy equivalence ie. E = mc^2 ,
This formula is given by Albert Einstein in 21 November 1905 , in the paper "Does inertia of a body depends upon its energy content"   mass energy equivalence is a product of the special theory of relativity and physicist Henry Poincaré described it as a paradox.
Mass energy equivalence is a very important principle of relativistic physics , which give a relation between mass and energy. This principle tell us that anything which have mass has an equivalent amount of energy and vice versa, vice versa means if mass contain energy then energy contain mass. And this fundamental quantities are related to each other by Einstein's famous formula ie. E = mc^2. Where c is speed of light ( c = ~3×10^8 m/s). According to this formula, if anyone wants to calculate the en…

GRAVITATIONAL LENSING, understanding the basic concepts.

Today in "Laws Of Nature" we are going to talk about a new concept ie. Gravitational lensing. Have you heard this term ever before, if not then, then you are at right place. Here you can understand everything about gravitational lensing, Such as -


what is Gravitational lensing?, how can Gravitational field form lens ? , How is this lens is different from the lens , which we have read in ray optics. (ie. Convex and concave lens), which type of lens is formed by Gravitational field? Does it is convex or concave.? So let's explore what is Gravitational lensing?
 Before going further in the article let's take a historical look on this concept.  The concept of Gravitational lensing was first introduced by the physicist Orest Chvolson (1924) and Frantisek link (1936), these two mens are credited for first to discuss on this effect in print. But this effect is commonly associated with the Albert Einstein, who has published an article on this subject in 1936.

We know that ou…

GALILEANS & LORENTZ TRANSFORMATIONS | The basic mathematical operations for the special theory of relativity.

Today we are going to talk about a very important concepts that is the GALILEANS & LORENTZ TRANSFORMATIONS. And this concept of transformation is very important for the mathematical explaination of relativistic physics. When Einstein put his special theory of relativity in September 1905. Then various new concept get born out of this theory, that is the time dilatation, length contraction , mass energy equivalence, relativistic mass. And all this new concept can only be explained by using mathematics. So today we are going to take a look on this foundation mathematics of special theory of relativity, without which special theory of relativity is somehow incomplete.
So Let's starts our talk with galilean transformation.
GALILEAN TRANSFORMATION Consider the two frame of reference S and S' having the coordinates of any point P is (x,y,z) and (x',y',z') , initially both frame of reference are at same position ie. concide to each other, where t is zero for both refe…

LENGTH CONTRACTION , A High Speed EFFECT, and understanding it's basic concepts.

Today we are going to talk about a very interesting concept of relativistic physics ie. THE LENGTH CONTRACTION, This concept is firstly postulated by George Fitzgerald and Hendrick Antoon Lorentz to explain the negative outcome of Michelson - Morley experiment and rescue the hypothesis of stationary aether.
But when Albert Einstein put his the special theory of relativity in September 1905.
Length contraction become a clear topic , because this contraction can be easily explained by using the special theory of relativity.
The second postulate in the special theory of relativity says that the speed of light in the  vaccum is constant for all observers, regardless the motion of light source an observer, but you have to remember that any observable mass can't travel with the speed of light.
but what would happened to the object which is moving with the speed of light. If a object is travelling with c then some physical dimensions of the object changes.
The physical dimensions which …

TIME DILATION , The key point to TIME TRAVEL, understanding the basic concepts.

Today we are going to talk about a very  interesting phenomenon, which has come into existence with the Einstein's special theory of relativity. We are not talking about any other things, we are only talking about THE TIME DILATION.
In the special theory of relativity Albert Einstein shows that time is a relative quantity. According to the Einstein the flow of time is same as the flow of river, we know that sometimes river flow fast and sometimes this river flows slower. Exactly same as river, time also flow sometimes fast and sometimes slow.  But when does time flow slower and faster? This is the question. In the form of answer, it's one explaination is in the special theory of relativity, and one explaination is in the general theory of relativity. According to the Special theory of relativity (STR), slowance and fastance of time only depends on the speed of the object.                   T = D/S  If speed is very large then time becomes very slow or you can say very small. …

THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.

Today we are going to talk about a very important and revolutionary concept that is THE GENERAL THEORY OF RELATIVITY.
This theory came into existence after 10 years of special theory of relativity (1905), and published by Albert Einstein in 1915.
This theory generalise the special theory of relativity and refines the Newton's laws of universal gravitation.
After coming this theory people's perspective about space and time has been changed completely. And this theory give a new vision to understand the spacetime geometry.
This theory gives a unified description of gravity as a geometrical properties of space and time.
This theory helps us to explain some cosmological phenomenon that is ,

* why small planets revolve around the big stars?
* Why everything in this universe is keep moving?
* Why mostly planets and stars are spherical in shape?
* Why does gravity create?
* Why does time become slow near the higher gravitating mass. Ie. Gravitational time dilation.
And gravitational…

THE SPECIAL THEORY OF RELATIVITY | understanding the basic concepts.

Today we are going to talk about a very interesting concept of classical mechanics,
And which topic we are going to talk about today, is always being a subject of discussion so far. Most of the people can't understand this concept after reading once, but today we are going to talk about this with a simplified explanation... If you want to understand then read it till end.
We are talking about , THE SPECIAL THEORY OF RELATIVITY. Which are originally proposed by the genius Albert Einstein in 26 September 1905 with the title of  " ON THE ELECTRODYNAMICS OF MOVING BODY". And it is generally accepted and experimentally confirmed physical theory.
After coming this theory , the way of watching the universe has been changed completely.
If we want to understand this theoretical concept. Then we have to start it from starting point. Then let's start...
Going further in the article , we have to take a look at the basic idea behind this theory , which is termed as the postulate…

5G A NEW ERA OF CONNECTIVITY | features , coverage, scalability, latency and internet of things (IoT).

Today we are going to talk about a upcoming technology ie. 5G (fifth Generation mobile internet connectivity) many of you must hearing about the 5G, and many of you may thinking that, what is 5G? , and how is this going to effect us? And after launching this connectivity what changes we are going to see?
If this type of questions are revolving in your mind then you are at authentic place , here you can access all information about 5G.
So let's start reading...
As IT sector and telecom companies are developing their technologies , by the way mobile internet connectivity are also developing. And 5G is the result of this type of development. 5G covers a long distance of network generation. 5G or fifth Generation wireless network came after 1G, 2G, 3G and 4G networks. Each generation of mobile network has its own characteristics features of speed, latency, scalability and coverage. Take a brief look on this features,

SPEED  it is the quantity of the information that a network can tran…

AVERAGE Problems tricks | fast track arithmetic formulae for problem solving. for all competitive examination//

Today in "laws of nature" we are going to talk about the very important arithmetic formulae on AVERAGE , which are very helpful for all types of competitive examination.
AVERAGE PROBLEM SOLVING TRICKS
1). If the number of the quantities and it's sum is given then the average is given by = sum of the quantities/no. of the quantities

2). If the no. of the quantities and it's average is given then the sum of the quantities is = no. of the quantities × it's average.

3). If the sum and it's average is given then the the no. of the quantities is = sum of the quantities/ average

4). If the average of A boys is x , and the average of B girls is y, if all of them is put together , then average is = (Ax + By)/(A+B)

5). If average of A boys is x , and average of B boys out of A boys is y then average of rest boys is = (Ax-By)/(A-B)

6). If the average of A objects is x , if any object is removed from the list then average become y then the magnitude of removed object is …

Why does GHOST become more powerful after death? Understanding the ghost behaviour.

Today  in "Laws Of Nature" we are going to talk about the concept of ghost,the topic of ghost are very popular across the globe,and every country wants to talk about this mysterious happening, which are related to some supernatural power.
But today we are living in the world of science and technology, and before agreeing on any concept,we want some reasons to prove it, because science says that for every happening there is a certain reason.

But in this world some topics are so mysterious, terrifying and unbelievable that science are also not able to answer this,so science doesn't research more on this type of topic, and finally science says that ghost type of things doesn't exist.
But according to the paranormal investigators existence of ghost are real, many paranormal investigators says that they have captured the real pictures of ghost, and this pictures clearly tell us about the presence of ghost.
But do you know why ghost exis,
According to many spiritual books…

Archimedes principle , understanding the basic concepts and it's explanation.

Today we are going to talk about the concept of Archimedes principle, this is a very important and interesting phenomenon of hydrostatic.
There are lot of application of this principle in our daily life. Some application are list below:
1). The floatation of boat and ships on the surface of water.
2). Upward motion of air bubbles in the water.
3). Sudden upthrust in a mug when it is dipped perpendicularly in the water.
4). Not sinking of a air filled balloon if it is dipped in the water , and many more application can be found if we start searching in our surroundings.
So, question is what Archimedes principle states?
If we talk about it then Archimedes principle simply states that if a object is immersed fully or partially in the fluid (liquid or gas) then it suffer a upward buoyant force, that is equal the weight of the fluid which object displaced. This concept is given by a Greek philosopher Archimedes in 250 BCE

A SIMPLIFIED EXPLAINATION

When a object is immersed fully or partial…

capillary action, understanding the basic concepts and it's ascent Derivations.

Today we are going to talk about the concept of capillarity. It is a very important and interesting concept of hydrodynamics.
This concept have many applications in our daily life such as:
1). Absorption of ink by blotting paper is due to capillary action, because blotting paper have pores which absorb the ink and slowly slowly ink rises.
2). The rising of oil through the wick of the lamp is also a capillary action.
3). The upper portion of the trees gets its water and food due to capillarity.
4). The absorption of water by the towel after bathing is due to capillarity.
5). The rising of water in the handpump is also a capillary action.
There are many applications of capillarity in our surroundings if we watch carefully.
So after going further in the article, we have to understand the meaning of capillarity first. Capillary is taken from a Latin word capila which means hair like. So capillary is regarded as a tube which is hair like thin, and it's radius is very small.
And capill…