Jagat Singh

Introduction to vectors

Some Basic Concepts

Types of Vectors

Addition of Vectors

Multiplication of a Vector by a Scalar

Components of a vector

Vector joining two points

Section formula

Product of Two Vectors

Scalar (or dot) product of two vectors
geometrical and mathematical meaning of dot product
Projection of a vector on another vector

angle between vectors

applications of dot product


Vector (or cross) product of two vectors
geometrical and mathematical meaning of cross product and 

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IIT JEE

JEE Main and Advanced Preparation

English

Vector Algebra for IIT JEE

Vectors

Vectors and Three Dimensional Geometry

Mathematics

IITJEE, NEET UG and Foundation

Ace the toughest competitive and government exams in India 

Test Preparation

Introductiion

Some Basic Concepts

Types of Vectors

Addition of Vectors

Multiplication of a Vector by a Scalar

Components of a vector

Vector joining two points

Section formula

Product of Two Vectors

Scalar (or dot) product of two vectors

Projection of a vector on a line

Vector (or cross) product of two vectors

Course overview

Learn about quantities and theor difference.
Basics of vectors
A scalar quantity is a one dimensional measurement of a quantity, like temperature, or mass. A vector has more than one number associated with it. A simple example isvelocity. It has a magnitude, called speed, as well as a direction, like North or Southwest or 10 degrees west of North

And formation of vectors , position vectors and much more

Vector and its formation

Length of a vector or magnitiude of a vector and how to evalute its value.
Draw a vector triangle. When you draw the horizontal and vertical components, you end up with a right triangle. The magnitude of the vector is equal to the hypotenuse of the triangle so you can use the Pythagorean theorem to calculate it. Rearrange the Pythagorean theorem to calculate the magnitude.

Magnitude of vector and unit vector

Learn how to find direction ratios and direction cosines for a vector.
How to convert a given vector to unit vector to find its direction cosines.
Geometrical meaning of direction cosines and pyq on vector algebra
 Now that we have understood what direction cosines are, we can move to direction ratios. Any numbers that are proportional to the direction cosines are calleddirection ratios, usually represented as a, b, c. So we can write, a = kl, b = km, c = kn where k is a constant.

Direction ratios and Direction Cosines

vector algebra may mean: Linear algebra, specifically the basic algebraic operations of vector addition and scalar multiplication

Algebra of vectors

Dot product of two vectors ā and b is basically a scalar quantity that is equal to the sum of pair-wise products of coordinate vectors a and b. Dot product is also known as scalar productor inner product.
Learn how to find it and its geometrical meaninga and mathematical expression

Dot product and its expressions

Section formula, polygon law and tyoes of vectors


Let us consider that the line segment connecting P and Q is divided by a point R lying on PQ. The point R can divide the line segment PQ in two ways: internally and externally. Let us consider both these cases individually.

Case 1: Line segment PQ is divided by R internally

Let us consider that the point R divides the line segment PQ in the ratio m: n, given that m and n are positive scalar quantities we can say that,

mRQ¯¯¯¯¯¯¯¯ = nPR¯¯¯¯¯¯¯¯

Consider the triangles, ∆ORQ and ∆OPR.

RQ¯¯¯¯¯¯¯¯ = OQ¯¯¯¯¯¯¯¯ – OR¯¯¯¯¯¯¯¯ = b⃗  – r⃗ 
PR¯¯¯¯¯¯¯¯ = OR¯¯¯¯¯¯¯¯ – OP¯¯¯¯¯¯¯¯ = r⃗  – a⃗ 

Therefore,

m(b⃗  – r⃗ ) = n(r⃗  – a⃗ )

Rearranging this equation we get:

r⃗  = mb⃗ +na⃗ m+n

Therefore the position vector of point R dividing P and Q internally in the ratio m:n is given by:

OR→ = mb⃗ +na⃗ m+n

Case 2: Line segment PQ is divided by R externally

Let us consider that the point R divides the line segment PQ in the ratio m: n, given that m and n are positive scalar quantities we can say that,


mRQ¯¯¯¯¯¯¯¯ = -nPR¯¯¯¯¯¯¯¯

Consider the triangles, ∆ORQ and ∆OPR.

RQ¯¯¯¯¯¯¯¯ = OQ¯¯¯¯¯¯¯¯ – OR¯¯¯¯¯¯¯¯ = b⃗  – r⃗ 
PR¯¯¯¯¯¯¯¯ = OR¯¯¯¯¯¯¯¯ – OP¯¯¯¯¯¯¯¯ = r⃗  – a⃗ 

Therefore,

m(b⃗  – r⃗ ) = -n(r⃗  – a⃗ )

Rearranging this equation we get:

r⃗  = mb⃗ –na⃗ m–n

Therefore the position vector of point R dividing P and Q internally in the ratio m:n is given by:

OR→ = mb⃗ –na⃗ m–n

What if the point R dividing the line segment joining points P and Q is the midpoint of line segment AB?

In that case, if R is the midpoint, then R divides the line segment PQ in the ratio 1:1, i.e. m = n = 1.The position vector of point R dividing will be given as:

OR→ = b⃗ +a⃗ 2

Section formula, Polygon law

Properties of Dot product and its applications to solve questions asked in IIT JEE Exams , CBSE exams and other competitive exams.
With proofs for
Commutative law, Distributive law and magnitude value for addition and subtraction of vectors

Properties of dot product

Properties of dot product part 2

Linear combination of vectors
Linearly independent and dependent vectors,
Collinear and coppaner vectors
And much more in this lesson for iit jee math
If one vector is equal to the sum of scalar multiples of other vectors, it is said to be a linear combination of the other vectors.

For example, suppose a = 2b + 3c

Note that 2b is a scalar multiple and 3c is a scalar multiple. Thus, ais a linear combination of b and c.
Learn all about about 
For iit jee vectors mathematics

Linear combination of vectors

Cross product and its properties, finding vector perpendicular to two given vectors, angle between vectors , determinant method for vector product, application of vector product and properties explained in detail in this lesson

Cross product p1

Cross product and its properties, finding vector perpendicular to two given vectors, angle between vectors , determinant method for vector product, application of vector product and properties and finding area of triangle, parallelogram explained in detail in this lesson

Cross product p2

Quick approach to solve problems on vectors, dot product and cross product application and evaluation of cross and dot product with their use

Problems on product of vectors

Questions on vector triple product

Scaler triple product

Teaching - Physics & Quant
Founder - The VMD Inst, The VMD GYM, VIReAL Classrooms
Manager - Medical Edu Services Pvt Ltd

Uttam Singh

This lesson is made for a quick revision of Vectors for IIT JEE exam.

(Hindi) Vectors:IIT JEE NCERT (Revision)

My AIR IN JEE mains  2017 is 8005 and in JEE advance  is 8769 and my maths score in JEE advance is 97/124,I had qualified RMO in 2015.

Karan Kapoor

In this course Karan Kapoor will discuss all the topics of  vector which are syllabus of jee mains or jee advanced,i will also discuss ques related to each topic and previous year questions of jee mains and jee advanced

Vector for IIT JEE

BITS PILANI@CSE
JEE Mains 2019 AIR-1356 ( MATHS -120/120 [100 %ile] )
JEE Adv 2019 AIR-3370

Atishay Jain

This video series is based on the chapter 'vectors'. I will teach scalar product ,vector product , identities, questions ,etc. which is necessary for jee mains and advanced.

(Hindi) Vectors : IIT JEE

Teaching for more than 15 years in the field of IITJEE preparation and for indian statistical inst.Find me on YouTube-"AJITSHARMAMaths"

Kumar Ajit

Vector Algebra, geometrical interpretation of vectors

(Hindi) Vectors -Geometrical Applications

A Game Changer in Mathematics, produced multiple 100 percentilers, Air 33 & 34 (Main 2024), his courses are the Benchmark for IIT JEE 

Vineet Loomba

This course covers everything on Vectors for IIT-JEE (JEE Main and Advanced)

Lessons

15 lessons • 3h 19m

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Course overview

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Vector and its formation

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Magnitude of vector and unit vector

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Direction ratios and Direction Cosines

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Algebra of vectors

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Dot product and its expressions

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Section formula, Polygon law

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Properties of dot product

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Properties of dot product part 2

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Linear combination of vectors

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