# Ex 4.3, 2

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 4.3, 2 (Introduction) Show that points A (a , b + c), B (b,c + a), C (c,a + b) are collinear Ex 4.3, 2 Show that points A (a , b + c), B (b,c + a), C (c,a + b) are collinear Three point are collinear if they lie on some line ⇒ They do not form a triangle ⇒ Area of triangle = 0 We know that Area of triangle is given by ∆ = 12 x1y11x2y21x3y31 Here, x1 = a, y1 = b + c, x2 = b, y2 = c + a, x3 = c , y3 = a + b ∆ = 12 ab+c1bc+a1ca+b1 Applying C1 →C1 + C2 ∆ = 12 a+b+cb+c1b+c+ac+a1c+a+ba+b1 Taking (a + b + c) common from C1 ∆ = 12 (a + b + c) 1b+c11c+a11a+b1 Here, 1st and 3rd Column are Identical Hence value of determinant is zero ∆ = 12 (a + b + c) × 0 = 0 So, ∆ = 0 Hence points A, B & C are collinear

Ex 4.1, 7
Important

Example 14 Important

Example 15 Important

Example 16 Important

Ex 4.2, 7 Important

Ex 4.2, 8 Important

Ex 4.2, 11 Important

Ex 4.2, 12 Important

Ex 4.2, 13 Important

Ex 4.2, 14 Important

Ex 4.2, 15 Important

Example 18 Important

Ex 4.3, 2 Important You are here

Ex 4.3, 3 Important

Example 24 Important

Example 26 Important

Ex 4.5, 10 Important

Ex 4.5, 15 Important

Ex 4.5, 18 Important

Ex 4.6, 13 Important

Ex 4.6, 15 Important

Ex 4.6, 16 Important

Example 32 Important

Example 34 Important

Misc. 2 Important

Misc 11 Important

Misc. 15 Important

Misc. 16 Important

Misc. 19 Important

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.