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## Hsslive Guru Plus Two Maths Chapter 10 Vector Algebra: Hsslive Guru 12th Maths Chapter 10 Vector Algebra Malayalam Medium Notes & Solutions

 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 step-by-step 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 PDF Provider https://www.hssliveguru.org/

## 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.

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## 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

1. Equal Vectors: Vectors having same magnitude and direction regardless of the positions of their initial points.
2. Collinear Vectors: Vectors which are parallel to the same line, irrespective of their magnitude and direction.
3. Like and Unlike Vectors: Collinear vectors having same direction are like vectors and opposite direction are unlike vectors.
4. Unit Vectors: Vectors with magnitude unity.

II. Component form of a vector
Let i, j, k be the unit vectors along the x-axis, y-axis, z-axis 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¯¯¯¯¯¯¯¯.

AB¯¯¯¯¯¯¯¯+BC¯¯¯¯¯¯¯¯+CA¯¯¯¯¯¯¯¯=0¯¯¯ is known as triangle law of vector addition.

IV. Multiplication of a vector by a scalar
Let a¯ = a1i + a2j + a3k 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 λ|a¯|.
λa¯ = λa1i + λa2j + λa3k

V. Vector joining two points
If P(a1, a2, a3) and Q(b1, b2, b3) are two points, then the vector joining P and Q is the vector PQ¯¯¯¯¯¯¯¯.
ie: PQ¯¯¯¯¯¯¯¯ = (b1 – a1)i + (b2 – a2)j + (b3 – a3)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¯ = a1i + a2j + a3k; b¯ = b1i + b2j + b3k and c¯ = c1i + c2j + c3k, 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.

## FAQs about Hsslive Guru 12th Maths Chapter 10 Vector Algebra

#### Can I download Class 12th Maths Chapter 10 Vector Algebra Malayalam Medium Notes??

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