Chapter 11 Class 12 Three Dimensional Geometry
Ex 11.1, 2
Example, 6 Important
Example, 7
Example 10 Important
Ex 11.2, 5 Important You are here
Ex 11.2, 9 (i) Important
Ex 11.2, 10 Important
Ex 11.2, 12 Important
Ex 11.2, 13 Important
Ex 11.2, 15 Important
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 13 Important Deleted for CBSE Board 2024 Exams
Question 14 Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 4 (a) Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 12 Important Deleted for CBSE Board 2024 Exams
Question 14 (a) Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Question 19 Important Deleted for CBSE Board 2024 Exams
Question 20 Important Deleted for CBSE Board 2024 Exams
Misc 3 Important
Misc 4 Important
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 14 Important Deleted for CBSE Board 2024 Exams
Misc 5 Important
Question 16 Important Deleted for CBSE Board 2024 Exams
Chapter 11 Class 12 Three Dimensional Geometry
Last updated at April 16, 2024 by Teachoo
Ex 11.2, 5 Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2𝑖 ̂ − 𝑗 ̂ + 4𝑘 ̂ and is in the direction 𝑖 ̂ + 2 𝑗 ̂ − 𝑘 ̂ . Equation of a line passing though a point with position vector 𝑎 ⃗ and parallel to vector 𝑏 ⃗ is 𝒓 ⃗ = 𝒂 ⃗ + 𝜆 𝒃 ⃗ Here, 𝒂 ⃗ = 2𝒊 ̂ − 𝒋 ̂ + 4𝒌 ̂ & 𝒃 ⃗ = 𝒊 ̂ + 2𝒋 ̂ − 𝒌 ̂ So, 𝑟 ⃗ = (2𝒊 ̂ − 𝒋 ̂ + 4𝒌 ̂) + 𝜆 (𝒊 ̂ + 2𝒋 ̂ − 𝒌 ̂) ∴ Equation of line in vector form is (2𝑖 ̂ − 𝑗 ̂ + 4𝑘 ̂) + 𝜆 (𝑖 ̂ + 2𝑗 ̂ − 𝑘 ̂) Equation of a line passing though (x1, y1, z1) and parallel to a line having direction ratios a, b, c is (𝒙 − 𝒙𝟏)/𝒂 = (𝒚 − 𝒚𝟏)/𝒃 = (𝒛 − 𝒛𝟏)/𝒄 Since the line passes through a point with position vector 2𝒊 ̂ − 𝒋 ̂ + 4𝒌 ̂, ∴ 𝒙𝟏 = 2, y1 = −1, z1 = 4 Also, line is in the direction of 𝒊 ̂ + 2𝒋 ̂ − 𝒌 ̂, Direction ratios : 𝒂 = 1, b = 2, c = −1 Equation of line in Cartesian form is (𝑥 − 2)/1 = (𝑦 − ( −1))/2 = (𝑧 − 4)/( − 1) (𝒙 − 𝟐)/𝟏 = (𝒚 + 𝟏)/𝟐 = (𝒛 − 𝟒)/( − 𝟏)