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Lesson Posted on 24 Sep CBSE/Class 11/Science/Physics CBSE/Class 11/Science/Physics/Unit 2-Kinematics Exam Coaching/CET Coaching/Physics

Om Prakash Mishra

I am teaching Mathematics and Physics from past more than 12 years in coaching as well as home tuition...

Law of the addition of vectors (1) Parallelogram law of addition of vectors: It states that if two vectors are represented in direction and magnitude by two sides of a parallelogram, then their resultant is given by the diagonal passing through their common point. (2) Triangle law of addition of vectors If... read more

**Law of the addition of vectors**

**(1) Parallelogram law of addition of vectors:** It states that if two vectors are represented in direction and magnitude by two sides of a parallelogram, then their resultant is given by the diagonal passing through their common point.

**(2) Triangle law of addition of vectors**

If two vectors are represented in direction and magnitude by two adjacent sides of a triangle taken in the same order, then their resultant is given by the third side taken in opposite order.

**(3) Polygon law of addition of vectors**

If any number of vectors are represented in magnitude and direction by sides of a polygon taken in the same order, then their resultant is given by the closing side taken in opposite order.

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Comments Lesson Posted on 24 Sep IIT JEE/IIT - JEE Mains/Physics/Kinematics CBSE/Class 11/Science/Physics CBSE/Class 11/Science/Physics/Unit 2-Kinematics/Chapter 4-Motion in a Plane

Om Prakash Mishra

I am teaching Mathematics and Physics from past more than 12 years in coaching as well as home tuition...

Dot or Scalar Product of Vectors Dot Product of two vectors A and B is defines as product of magnitude of the vectors and cosine of the angle between them. A•B = |A||B|CosT, Where T is the angle between the vectors A and B. It is a scalar quantity Special Cases (I) If two vectors are perpendicular... read more

**Dot or Scalar Product of Vectors**

Dot Product of two vectors ** A **and **B **is defines as product of magnitude of the vectors and cosine of the angle between them.

**A•B = |A||B|CosT, **Where T is the angle between the vectors **A** and **B.**

It is a scalar quantity

**Special Cases**

(I) If two vectors are perpendicular to each other their dot product is Zero.

(ii) If two vectors **A **and B are parallel their dot product is |A||B|.

If **i, j, k **are unit vectorsalong X, Y, Z axis respectively then

**i.i = 1**

**j.j = 1**

**k.k = 1**

**i.j = 0**

**j.k = 0**

**K.i = 0. **

* Note : Scalar product is commutative *

*i.e. ***A.B = B.A**

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Comments Lesson Posted on 24 Sep CBSE/Class 12/Science/Mathematics/Unit IV: Vectors and Three-Dimensional Geometry/Vectors CBSE/Class 11/Science/Physics/Unit 2-Kinematics Vectors

Om Prakash Mishra

I am teaching Mathematics and Physics from past more than 12 years in coaching as well as home tuition...

Vector or Cross product of vectors It is defined as product of magnitude of the vectors and sine of the angle between them it is a vector quantity. For two vectors A and B A × B = |A||B| SinTn where T is the angle between the vectors A and B. and n is unit normal vector perpendicular to... read more

**Vector or Cross product of vectors **

It is defined as product of magnitude of the vectors and sine of the angle between them it is a vector quantity.

For two vectors **A** and **B **

**A × B = |A||B| **SinTn

where T is the angle between the vectors **A **and **B. **and **n **is unit normal vector perpendicular to both **A **and **B.**

This product is a vector quantity again which is in a plane perpendicular to both the given vectors.

• It is not anticommutative. i.e. **A×B =-B×A. **

If **i, j, k **are unit vectors along X, Y, Z axis respectively then .

**i×i = j×j = k×k = 0.**

**i×j = k**

**J×k = i**

**k×i = j**

**j×k = -k**

**k×j =-i**

**i×k =-i.**

** **

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Lesson Posted on 25 Sep CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Permutations and Combinations IIT JEE/IIT JEE MAINS IIT JEE/IIT - JEE Mains/Mathematics/Permutations and Combinations

Om Prakash Mishra

When things are arranged in a circle then number of permutations ( arrangements ) is calculated in the following way : Since one of the objects is always fixed in its position so the total number of objects to be arranged gets reduced by 1. So if total n objects are there then no of permutations will... read more

When things are arranged in a circle then number of permutations ( arrangements ) is calculated in the following way :

Since one of the objects is always fixed in its position so the total number of objects to be arranged gets reduced by 1.

So if total n objects are there then no of permutations will be

(1) when clockwise and anticlockwise permutations are counted different = (n-1)!

(2) when clockwise and anticlockwise are not counted different = (n-1)!/2

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Comments Lesson Posted on 21 Sep CBSE/Class 11/Science/Mathematics CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Permutations and Combinations Exam Coaching/CET Coaching/Mathematics

Om Prakash Mishra

Permutation means arrangement Fundamental principles of counting If a work can be done in m ways and the either can be done in n ways, then the no .of ways in which both the works can be done is m×n ways. But if they are done I depend on each other that is doing of one does not affect the other,... read more

Permutation means arrangement

Fundamental principles of counting

If a work can be done in m ways and the either can be done in n ways, then the no .of ways in which both the works can be done is m×n ways.

But if they are done I depend on each other that is doing of one does not affect the other, then it is m+n.

The no of ways in which n different things can be arranged is n! Which is equal to

n!=n ×(n-1)×.....×2×1.

The no. of ways in which r things out of n things can be arranged is

n^P^r = n!/(n-r)!.

If any particular object is repeated p, q.. times then the result is divided by p! q!... respectively to get the desired permutation.

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Comments 1 Lesson Posted on 16 Sep CBSE/Class 12/Science/Mathematics CBSE/Class 12/Science/Mathematics/Unit III: Calculus IIT JEE/IIT JEE MAINS/Mathematics

Om Prakash Mishra

To find maximum and minimum value of a given function. Differentiate the function first and then find the values of x at which the function becomes zero these are the possible points of Maximum and minimum values of the function then apply any of the following test (1) 1st derivative test: If at any... read more

**To find maximum and minimum value of a given function**.

Differentiate the function first and then find the values of x at which the function becomes zero these are the possible points of Maximum and minimum values of the function then apply any of the following test

**(1) 1st derivative test:** If at any of the above values of x dy/dX changes its sign from +ve to -ve then that is a point of local Maxima.

And if dy/dX changes sign from -ve to +ve that is a point of local minima.

**(2) 2nd derivative test:** Find the 2nd derivative and put the above values of x obtained if it comes -ve that is a point of local Maxima and if it comes +ve that's a point of local minima.

Note: there can be more than 1 point of local Maxima and Minima

**Global Maximum and Minimum**: put all the values of x obtained in the function and check which one is largest, that value correspond to Global Maxima and that vale is global maximum. Similarly check for Global minima.

**Note**:sometimes 2nd derivative test fails i.e it becomes zero that that point is called point of inflection. Then check with first derivative test.

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Answered on 25 Aug Exam Coaching/CET Coaching/Biology

Sec (90×1+30)

= - Cosec30

= - 2

Venky

MBA Home Tutor

-2

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Answers 2 Comments Lesson Posted on 27 Apr Tuition/BA Tuition/Advanced cell biology Biomolecules Tuition/MBBS & Medical Tuition/Physiology

Shivani Y.

Photosynthesis It is the process by which producers of the ecosystem fix atmospheric Carbon dioxide (CO2) from otherwise unavailable, inorganic, gaseous state of carbon(C) to usable organic form (carbohydrates). Many organisms can carry out photosynthesis, including both prokaryotic and eukaryotic Organisms... read more

**Photosynthesis**

It is the process by which producers of the ecosystem fix atmospheric Carbon dioxide (CO2) from otherwise unavailable, inorganic, gaseous state of carbon(C) to usable organic form (carbohydrates).

Many organisms can carry out photosynthesis, including both prokaryotic and eukaryotic Organisms for, eg. Cyanobacteria, Green Sulfur bacteria, Green non-sulfur bacteria etc. and

Algae, Plants respectively.

If we want to describe photosynthesis in layman's language, then it can be described as a word made up of 2 subwords that is photo + synthesis.

Where Photo= sunlight and Synthesis= to prepare something.

Thus photosynthesis is simply a process of preparation of the organic form of carbon (Carbohydrates) in the presence of sunlight or using energy from the sunlight and atmospheric CO2 as raw material.

Thus producers like plants and photosynthetic bacteria, bring the unusable form of C from the atmosphere to living system in a usable organic form.

**Photosynthesis can be of two types:**

- Anoxygenic photosynthesis
- Oxygenic photosynthesis

**Anoxygenic photosynthesis:**

As the name indicates Anoxy + genic where: Anoxy= without Oxygen; genic= generation

thus the type of photosynthesis where Oxygen is not generated and not evolved in the environment during the process of photosynthesis is called as Anoxygenic photosynthesis.

This type of photosynthesis is ancient and is the first type of photosynthesis used to occur when the earth's environment was reductive in nature, and respiration type was anaerobic.

Eg. Purple sulfur bacteria, green sulfur bacteria etc.

**Oxygenic photosynthesis:**

As the name indicates Oxy + genic where: Oxy= Oxygen; genic= generation

thus the type of photosynthesis where Oxygen is generated and evolved in the environment during the process of photosynthesis is called as Oxygenic photosynthesis.

This type of photosynthesis evolved when some of the producers like cyanobacteria got the ability to use water as an electron donor for the light reaction of photosynthesis to occur. Thus with the photolysis of water (H2O), Oxygen was generated and added to the environment.

This made earth's environment to become Oxidative from reductive in nature and making room for aerobic respiration to evolve further. Eg. Cyanobacteria, Algae, Plants.

In my next post, I will be covering the mechanism of photosynthesis.

Your feedback is important. Do comment your queries and suggestions.

Happy Learning

Shivani

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Comments Answered on 11 Apr Exam Coaching/CET Coaching

Sridhara KS

Tutor

Hello Aakash, Keep it simple intitally as to give 5 hours per day. Slowly and steadily increase that to around 12 hours perday at the end of your 1st PU. By the time you complete your second year, it should reach around 14 hours of work per day. 4 hours of work per day, does not mean it should be... read more

Hello Aakash,

Keep it simple intitally as to give 5 hours per day. Slowly and steadily increase that to around 12 hours perday at the end of your 1st PU. By the time you complete your second year, it should reach around 14 hours of work per day.

4 hours of work per day, does not mean it should be continious at a stretch. it can be a chunk of 1 hour or 2 hours. But the commitment should be 5 hours per day and it should be consistent enough.

All the best.

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Lesson Posted on 26 Mar CBSE/Class 12/Science/Mathematics Exam Coaching/CET Coaching Exam Coaching/CET Coaching/Mathematics

Goodwill Gate2iit

Goodwill Gate2iit is a joint initiative from IIT graduates. We specialize in tutoring students for...

Determine the co-ordinates (x,y) of foci for given parabola. y2 = 2(x-1)

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