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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…

Hydrodynamics : fluid at motion , study notes for IIT JEE | concept booster, chapter highlights |

HYDRODYNAMICS : FLUID IN MOTION
FLUID MOTIONSTREAMLINE FLOWIt is the type of flow in which the path taken by the fluid particles under a steady flow is streamline in the direction of the fluid velocity at that point. LAMINAR FLOW
In this type of flow, fluid flows in steady state and moves in the form of layers of different velocities and never intermix while flowing. TURBULENT FLOW
It is also a type of the fluid motion in which velocity of the particles is greater than its critical velocity and particles become irregular during motion. CRITICAL VELOCITYIt is the maximum velocity of the fluid up to which the flow is streamline and above which it become turbulent is called critical velocity.
Mathematically ; Vc = kη/ρr , where η is viscosity of liquid, ρ  is the density of the liquid, r is the radius of the tube. REYNOLDS NUMBERIt is the number scale which determines the nature of the motion of the liquid through the pipe. Reynolds number is given as- = (Inertial force per unit area/viscous force …

Hydrostatic : fluids at rest | concept booster , chapter highlights | study notes for IIT JEE |

HYDROSTATIC : FLUIDS AT REST
PRESSURE DUE TO LIQUID*. Pressure is thrust applied by the liquids at rest per unit surface area of the objects when it is in contact with the liquid. If F is the force applied by the liquid on the small surface area of ∆A then Pressure is given in the form of limit as follows :
*. In CGS system unit of pressure is dyne/cm^2 and in SI system it is N/m^2. A pressure of one  N/m^2 is called a Pascal.
PASCAL LAW Pascal law states that pressure applied by a enclosed liquid is transmitted equally in all directions , to every position of the liquid and wall of the container. HYDROSTATIC PRESSURE OF A LIQUID COLUMN*. Pressure is given as = force / area = ρgh Where ρ is the liquid density and h is height of the liquid column.
*. All hydraulic press and brakes are based on Pascal law.
*. Unit of pressure is Pascal and it denoted as Pa.
*. 1 Bar = 10^5 Pa and 1 torr = 1 mm of Hg. DENSITY AND RELATIVE DENSITY*. Density is given by = mass /volume For water it is = 10^3 kg / m^3  1…

What happened to our solar system, if the mass of the Jupiter became as equal to the mass of the sun?

What if ! The mass of the Jupiter became as equal to the mass of the sun? All we know that our solar system have 8 planets and a sun. Among all the planets Jupiter has the largest mass or you can say Jupiter is the second largest mass body in our solar system.

Now let's imagine a situation in our solar system that, what will happened if the mass of the Jupiter became equal to the mass of the sun?
According to the general theory of relativity universe is infinitely stretched space time fabrics on which all the celestial bodies are kept. All the celestial bodies which are in the outer space haves different masses, so due to their different masses, the depression in the space time fabrics are also different. However here masses of Jupiter and sun are equal then the depression in the space time fabrics are also equal. Below some high probable possibilities are given on the basis of the imagination. If the mass of the Jupiter been equal to the mass of the sun.If the masses of the Jupiter an…

GRAVITATION study notes for IIT JEE | concept booster , chapter highlights , LAWS OF NATURE

GRAVITATIONNEWTON'S LAWS OF GRAVITATIONThis laws states that every body in the universe attract another body with a force which is directly proportional to product of the their masses and inversely proportional to the square of distance between them act along the line joining the two bodies. According to this law-  F = GMm/r^2 , where G is the proportionality constant called universal Gravitational constant. This universal Gravitational constant G is a scaler quantity. This constant remains same or unchanged in this entire universe , and it is independent of the shape , size and nature of the object and also independent of the intervening medium and temperature of the bodies.Value of G is in SI system is 6.67×10^-11Nm^2/kg^2. and value of G in CGS system is 6.67×10^-8 dye.cm^2/g^2Dimensional formula of G is[M^-1.L^3T^-2]Gravitational force between the two bodies is equal in magnitude but in opposite directions , hence it obeys the Newton's third law of motion. It forms action rea…

Heat Transfer | concept booster , study notes for IIT JEE |

HEAT TRANSFER*. Heat is the form of energy which flows from one body to another body in the form of radiation, molecular vibrations and molecular displacement. The mode of heat flow from this method are collectively known as heat transfer.
*. There are three mode of heat transfer. 1). Conduction  2). Convection 3). Radiation
*. THERMAL CONDUCTIVITY - It is the ability of the material to conduct heat from them.
*. HEAT CONDUCTION - It is time rate of flow of heat through any material for a given temperature difference.
*. The rate of heat transfer through a metal rod of length L and cross sectional area A and the temperature at the ends are T1 and T2 is -
 Rate of heat transfer = ∆Q/∆t = KA(T1-T2)/L    H = KA∆T/L and also H = Q/t So then Q = KA∆T.t/L Where K is called the cofficient of thermal conductivity. SI unit of K is J/smK or W/mK The term ∆T/L is called temperature gradient.
*. The rate of flow of heat = heat current or thermal current, and it is denoted by H. H = ∆Q/∆t = KA(T1-T2)/L = T1-T2/(…

Thermal properties of matter.| Concept booster , chapter highlights, study material for IIT JEE , NEET ETC.| LAWS OF NATURE

THERMAL PROPERTIES OF MATTER HEAT AND TEMPERATURE
*. Temperature is the measure of degree of hotness or coldness. *. If two body have tempt T1 and T2, if T1 > T2 then T1 is hotter than T2. *. Heat is the form of energy which flows from hotter body to colder body by virtue of its temperature difference. *. Transfer of heat is a non mechanical process. *. It's unit is joule (J) and sometimes uses calories (cal). 1 joule equal to 4.2 calorie. *. According to calorific theory of heat - heat is invisible , colourless, odourless and weightless fluid called caloric ,which flow from hotter body to colder body. *. According to dynamic theory of heat-  all substance (solid, liquid and gases) are made up of molecules. Depending upon the nature and tempt of materials they posses three different types of motion. 1). Translatory motion  2). Vibrational motion 3). Rotational motion
*. Temperature is commonly measured by thermometers. *. It has different units like Kelvin(K) , degree Celsius (°C) , Fahrenh…

Why does wires get hot or even melts, when a high current flow through them.?

HOW DOES RESISTANCE PRODUCED IN WIRES?
Resistance is the very important term/topic of current electricity. Without resistance imagination of electric physics is just a time waste.  So today we will talk about resistance in detail , so tuned with us till end- Let's start with a question , what is resistance? And why is it time waste , to imagine electric physics without resistance?  Before I start talking about resistance, you need to know that, how does electron flow in the wires? If you think it should be known , then go through the link to know this. How does electrons flow in the wires?

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Alternating current concept booster

Electromagnetic induction fast track revision

DOPPLER EFFECT EXPLAINATION
So what is resistance? And how does it create? Resistance is just like opposing something and this something is usually velocity. Did you ever run a bycle in opposite direction of wind flow. If yes then what happened to your velocity, it must be slo…

what is potential difference? and why is it important in current electricity?

The concept of potential difference is very important topic of current electricity. If you didn't know or understand this topic, then it is very difficult for you to give the explaination of the question, why does electrons move in electrical circuit after supplying electricity?So it is very important to understand the underlying concept of potential difference. Once you understand the concept of potential difference , then you are able to give the answers of various questions of current electricity. So let's starts with a question. What is the main purpose of electricity? Many of you can give the different answers, but If we talk about the main purpose of electricity then the main purpose of electricity is to create potential difference in the electrical circuits. All the big machine which are run on electricity, the source do nothing but they only create potential difference and all the rest activity( motion of electron and creation of current and many more)  is done my potent…

PROFIT and LOSS for competitive examination, shortcut tricks , fast track formulae

 PROFIT AND LOSS SOME IMPORTANT SUTRAS
*. Profit = selling price - cost price  *. Loss = cost price - selling price *. Cost price = selling price - profit *. Cost price = selling price + loss *. Selling price = cost price + profit *. Selling price = cost price - loss *. Profit percent = profit × 100/cost price *. Loss percent = loss ×100/cost price *. Cost price = SP ×100/(100+P) *. Cost price = SP ×100/(100 - L) *. Selling price = CP(100+P)/100 *. Selling price = CP(100-L)/100
*. If a dishonest sellsman sell his goods on CP but he uses fake weight instead of original weight , then the profit percent =      100(original weight - fake weight)/fake weight
*. If a dishonest sellsman use x% less weight, but he also sells his goods at y% profit/loss, then net percentage profit/loss = (+-y+x)100/100-x
*. If a sellsman wants to earn b% profit after selling his goods at a% discount , then the sufficient increment in the marked price of the goods is = 100(b+a)/100-a
*. If P sells a object to Q at a% profit/loss…

The concept of projectiles | Derivations for time of flight , maximum height , horizontal range , trajectory of a projectile.

THE PROJECTILE MOTION It is the type of motion in which if any object is fired with some initial velocity near the earth surface , then it's motion follows a curved path called projectile motion. This curved path by the objects is called the trajectory of the projectile. Any missiles which follows these path called ballistic missiles.
SOME EXAMPLES
*. When we throw a ball. * Firing of a missile. *. Path of the water which is flowing from the hole of a tank. *. Motion of a bullet. etc
SOME ASSUMPTIONS IN THE STUDY OF PROJECTILE MOTION
*. Zero air resistance. *. Effect of earth rotation on the object is negligible. *. Constant acceleration due to gravity.
EQUATION OF THE TRAJECTORY
MOTION IN HORIZONTAL DIRECTION
The velocity of the object in horizontal direction is constant, so it's acceleration is zero. The position of the object at any time t in the horizontal direction is-
 x = x0 + (ux)t + 1/2(ax)t^2 ,  [ux and ax is horizontal velocity and acceleration] But x0 = 0 , ux = ucosθ , ax = 0 ,…