Last updated at March 11, 2017 by Teachoo

Transcript

Ex 10.3, 2 Find the angle between the vectors 𝑖 − 2 𝑗 + 3 𝑘 and 3 𝑖 - 2 𝑗 + 𝑘 Let 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘 = 1 𝑖 − 2 𝑗 + 3 𝑘 and 𝑏 = 3 𝑖 − 2 𝑗 + 𝑘 = 3 𝑖 − 2 𝑗 + 1 𝑘 We know that 𝑎 . 𝑏 = 𝑎 𝑏 cos θ ; θ is the angle between 𝑎 & 𝑏 Now, 𝒂. 𝒃 = (1 𝑖 − 2 𝑗 + 3 𝑘). (3 𝑖 − 2 𝑗 + 1 𝑘) = 1.3 + (−2).(−2) + 3.1 = 3 + 4 + 3 = 10 Magnitude of 𝑎 = 12+ −22+32 𝑎= 1+4+9 = 14 Magnitude of 𝑏 = 32+ −22+12 𝑏= 9+4+1 = 14 Now, 𝑎 . 𝑏 = 𝑎 𝑏 cos θ 10 = 14 × 14 x cos θ 10 = 14 × cos θ cos θ = 1014 θ = cos-1 𝟓𝟕 Thus, the angle between 𝑎 and 𝑏 is cos-1 57

Ex 10.2, 7
Important

Ex 10.2, 9 Important

Ex 10.2, 10 Important

Ex 10.2, 13 Important

Ex 10.2, 17 Important

Example 14 Important

Example 16 Important

Example 21 Important

Ex 10.3, 2 Important You are here

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

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.