Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra: Hsslive Guru 12th Maths Chapter 10 Vector Algebra Malayalam Medium Notes & Solutions 
Hsslive Guru 12th Maths Chapter 10 Vector Algebra Malayalam Notes and Solutions: Students can download and check HssliveGuru.org Plus Two Maths Chapter 10 Vector Algebra notes pdf from the links provided in this page. All Students are requested to kindly go through the complete article to get the detailed information. We are also providing the Hsslive Guru Maths Chapter 10 Vector Algebra 12th malayalam medium solutions that too chapter wise in the below article. Maths Chapter 10 Vector Algebra is an important subject for 12th class exams, so students need to prepare carefully for the upcoming exams.
Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Notes & Solutions
Hsslive Guru Class Plus Two Maths Chapter 10 Vector Algebra solutions provide a solid conceptual base for all the topics included in SCERT Class Plus Two Maths Chapter 10 Vector Algebra Syllabus. It covers all the important theorems and formulae with detailed explanations to promote a better conceptual understanding in students. Hsslive Guru 12th Maths Chapter 10 Vector Algebra malayalam medium notes will help students in the preparation of upcoming exams in the best possible way.
HssliveGuru.org 12th Maths Chapter 10 Vector Algebra Malayalam Medium Notes
Hsslive Guru brings you SCERT Solutions for Plus Two Maths Chapter 10 Vector Algebra, designed by our subject experts to facilitate smooth and precise understanding of concepts. These Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Solutions of SCERT have detailed stepbystep explanations of problems given in the textbooks.
Board 
Kerala Board 
Class 
Plus Two 
Subjects 
Mathematics 
Chapters 
Maths Chapter 10 Vector Algebra 
Study Material 
Notes & Solutions 
Medium 
Malayalam/ English 
Format 

Provider 
Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Chapters List
These are all the chapters present in Hsslive Guru 12th Maths Chapter 10 Vector Algebra notes. We and our expert faculties have prepared the notes and solutions for each of these chapters which are provided below in this article.
How to download Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Chapter Wise Solutions?
 Visit the website of Hssliveguru.org.
 Look for Hsslive Guru 12th Class Notes and solutions.
 Now look for your preferred subject.
 Visit the post of Hsslive Guru 12th Maths Chapter 10 Vector Algebra Malayalam medium notes and solutions.
 Open the post and now look for links to download the solutions.
Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Chapter Wise Malayalam Medium Notes & Solutions
Students can download Hsslive Guru 12th Maths Chapter 10 Vector Algebra chapter wise solutions for the exercise present in the SCERT textbook using the links provided below:
Introduction
Physical quantities we deal are of two types, one that can be specified using a single real number which gives its magnitude and the other which involves the idea of direction as well as magnitude. The first type is called scalar quantity and the second is vector quantity. In this chapter we analyses the basic concepts about vectors, various operations, and their algebraic and geometrical properties.
I. Types of vectors
 Equal Vectors: Vectors having same magnitude and direction regardless of the positions of their initial points.
 Collinear Vectors: Vectors which are parallel to the same line, irrespective of their magnitude and direction.
 Like and Unlike Vectors: Collinear vectors having same direction are like vectors and opposite direction are unlike vectors.
 Unit Vectors: Vectors with magnitude unity.
II. Component form of a vector
Let i, j, k be the unit vectors along the xaxis, yaxis, zaxis respectively. The point P(x, y, z) be a point in space. Then the position vector of the point P can be expressed in component form as
1. If li + mj + nk is unit vector, then l,m,n are direction cosines along the vector.
2. If P (a, b, c) is a point on space, then a, b, c are direction ratios and
are direction cosines along the vector OP¯¯¯¯¯¯¯¯.
III. Addition of Vectors
AB¯¯¯¯¯¯¯¯+BC¯¯¯¯¯¯¯¯+CA¯¯¯¯¯¯¯¯=0¯¯¯ is known as triangle law of vector addition.
IV. Multiplication of a vector by a scalar
Let a¯ = a_{1}i + a_{2}j + a_{3}k be a vector and λ be a scalar. Then the product of the vector a¯ by a scalar is denoted by λa¯ and the new vector formed has a magnitude λa¯.
λa¯ = λa_{1}i + λa_{2}j + λa_{3}k
V. Vector joining two points
If P(a_{1}, a_{2}, a_{3}) and Q(b_{1}, b_{2}, b_{3}) are two points, then the vector joining P and Q is the vector PQ¯¯¯¯¯¯¯¯.
ie: PQ¯¯¯¯¯¯¯¯ = (b_{1} – a_{1})i + (b_{2} – a_{2})j + (b_{3} – a_{3})k
VI. Section Formula
If a¯ and b¯ be the position vectors of the points A and B respectively, then the position vector of the point P which divides AB in the ratio l:m
VII. Dot (Scalar) Product of vectors
VIII. Cross (vector) Product of Vectors
 a¯×b¯ is a vector perpendicular to a¯ and b¯.
 a¯×b¯ gives the area of a parallelogram with adjacent sides a¯ and b¯.
 i × i = j × j = k × k = 0,
 i × j = k, j × k = i, k × i = j
 j × i = k, k × j = i, i × k = j
IX. Box (Scalar Triple) Product of Vectors
Properties:
1. Since b¯×c¯ is a vector, [a¯b¯c¯] is a scalar quantity.
2. [a¯b¯c¯] is the volume of the parallelopiped with a adjacent sides vector a¯,b¯,c¯.
3. If a¯ = a_{1}i + a_{2}j + a_{3}k; b¯ = b_{1}i + b_{2}j + b_{3}k and c¯ = c_{1}i + c_{2}j + c_{3}k, then
4. if a¯,b¯,c¯ be any three vectors, then [a¯b¯c¯] = [b¯c¯a¯]=[c¯a¯b¯] (cyclic permutation of three vectors does not change the value of the scalar triple product).
5. In scalar triple product, the dot and cross can be interchanged.ie,
6. If any two vectors are interchanged the sign of box product is changed but magnitude remains the same.
7. If any two vectors are equal or proportional then the value of box product is zero.
8. Three vectors a¯,b¯,c¯ are coplanar if and only if [a¯b¯c¯] = 0.
Hsslive Guru Plus Two Maths Notes
 Hsslive Guru Plus Two Maths Notes
 Hsslive Guru Plus Two Maths Chapter 1 Relations and Functions Notes
 Hsslive Guru Plus Two Maths Chapter 2 Inverse Trigonometric Functions Notes
 Hsslive Guru Plus Two Maths Chapter 3 Matrices Notes
 Hsslive Guru Plus Two Maths Chapter 4 Determinants Notes
 Hsslive Guru Plus Two Maths Chapter 5 Continuity and Differentiability Notes
 Hsslive Guru Plus Two Maths Chapter 6 Application of Derivatives Notes
 Hsslive Guru Plus Two Maths Chapter 7 Integrals Notes
 Hsslive Guru Plus Two Maths Chapter 8 Application of Integrals Notes
 Hsslive Guru Plus Two Maths Chapter 9 Differential Equations Notes
 Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra Notes
 Hsslive Guru Plus Two Maths Chapter 11 Three Dimensional Geometry Notes
 Hsslive Guru Plus Two Maths Chapter 12 Linear Programming Notes
 Hsslive Guru Plus Two Maths Chapter 13 Probability Notes
0 comments:
Post a Comment