Last updated at March 11, 2017 by Teachoo

Transcript

Ex 10.2, 17 Show that the points A, B and C with position vectors, 𝑎 = 3 𝑖 − 4 𝑗 − 4 𝑘, 𝑏 = 2 𝑖 − 𝑗 + 𝑘 and 𝑐 = 𝑖 − 3 𝑗 − 5 𝑘 , respectively form the vertices of a right angled triangle. Position vectors of vertices A, B, C of triangle ABC are 𝑎 = 3 𝑖 − 4 𝑗 − 4 𝑘, 𝑏 = 2 𝑖 − 1 𝑗 + 1 𝑘 𝑐 = 1 𝑖 − 3 𝑗 − 5 𝑘 We know that two vectors are perpendicular to each other, i.e. have an angle of 90° between them, if their scalar product is zero. So, if CA. AB = 0, then CA ⊥ AB & ∠ CAB = 90° Now, AB = 𝑏 − 𝑎 = (2 i − 1 j + 1 k) − (3 i − 4 j − 4 k) = (2 − 3) i + (−1 + 4) j + (1 + 4) k = –1 i + 3 j + 5 k BC = 𝑐 − 𝑏 = (1 i − 3 j − 5 k) − (2 i − 1 j + 1 k) = (1 − 2) i + (−3 + 1) j + (−5 − 1) k = -1 i − 2 j − 6 k CA = 𝑎 − 𝑐 = (3 i − 4 j − 4 k) − (1 i − 3 j − 5 k) = (3 − 1) i + (−4 + 3) j + (−4 + 5) k = 2 i − 1 j + 1 k Now, 𝐀𝐁 . 𝐂𝐀 = (–1 i + 3 j + 5 k) . (2 i − 1 j + 1 k) = (−1 × 2) + (3 × −1) + (5 × 1) = (−2) + (−3) + 5 = −5 + 5 = 0 So, AB. CA = 0 Thus, AB and CA are perpendicular to each other. Hence, ABC is a right angled triangle.

Ex 10.2, 7
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Ex 10.2, 9 Important

Ex 10.2, 10 Important

Ex 10.2, 13 Important

Ex 10.2, 17 Important You are here

Example 14 Important

Example 16 Important

Example 21 Important

Ex 10.3, 2 Important

Ex 10.3, 3 Important

Ex 10.3, 10 Important

Ex 10.3, 13 Important

Ex 10.3, 16 Important

Example 23 Important

Example 24 Important

Example 25 Important

Ex 10.4, 2 Important

Ex 10.4, 5 Important

Ex 10.4, 9 Important

Ex 10.4, 10 Important

Ex 10.4, 11 Important

Example 28 Important

Example 29 Important

Example 30 Important

Misc 6 Important

Misc 12 Important

Misc 13 Important

Misc 15 Important

Misc 19 Important

Class 12

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

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .