Ex 11.2

Ex 11.2, 1

Ex 11.2, 2

Ex 11.2, 3 Important

Ex 11.2, 4

Ex 11.2, 5 Important

Ex 11.2, 6

Ex 11.2, 7 Important

Ex 11.2, 8

Ex 11.2, 9 Important You are here

Ex 11.2, 10 (i) Important

Ex 11.2, 10 (ii)

Ex 11.2, 11 (i) Important

Ex 11.2, 11 (ii)

Ex 11.2, 12 Important

Ex 11.2, 13

Ex 11.2, 14 Important

Ex 11.2, 15 Important

Ex 11.2, 16

Ex 11.2, 17 Important

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

Last updated at Feb. 1, 2020 by Teachoo

Ex 11.2, 9 Find the vector and the Cartesian equations of the line that passes through the points (3, – 2, – 5), (3, – 2, 6).Vector Equation Vector equation of a line passing through two points with position vectors 𝑎 ⃗ and 𝑏 ⃗ is 𝑟 ⃗ = 𝑎 ⃗ + 𝜆 (𝑏 ⃗ − 𝑎 ⃗) Given, the two points are So, 𝑟 ⃗ = (3𝑖 ̂ − 2𝑗 ̂ − 5𝑘 ̂) + 𝜆 ["(3" 𝑖 ̂−"2" 𝑗 ̂+"6" 𝑘 ̂")" −"(3" 𝑖 ̂−"2" 𝑗 ̂ −"5" 𝑘 ̂")" ] = 3𝑖 ̂ − 2𝑗 ̂ − 5𝑘 ̂ + 𝜆 ["(3" −3")" 𝑖 ̂−"(2" −(−2))𝑗 ̂+(6−(−5))𝑘 ̂)] A (3, − 2, − 5) 𝑎 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ − 5𝑘 ̂ B (3, − 2, 6) 𝑏 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ + 6𝑘 ̂ = 3𝑖 ̂ − 2𝑗 ̂ − 5𝑘 ̂ + 𝜆 [0𝑖 ̂ + 0𝑗 ̂ + 11𝑘 ̂] = 3𝒊 ̂ − 2𝒋 ̂ − 5𝒌 ̂ + 𝜆 (11𝒌 ̂) Therefore, the vector equation is 𝑟 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ − 5𝑘 ̂ + 𝜆 (11𝑘 ̂) Cartesian equation Cartesian equation of a line passing through two points A(x1, y1, z1) and B (x2, y2, z2) is (𝑥 − 𝑥1)/(𝑥2 − 𝑥_1 ) = (𝑦 − 𝑦1)/(𝑦2 − 𝑦1) = (𝑧 − 𝑧1)/(𝑧2 − 𝑧1) Since the line passes through A (3, −2, −5) x1 = 3, y1 = −2, z1 = − 5 And also passes through B (3, −2, 6) x2 = 3, y2 = −2, z2 = 6 Equation of line is (𝑥 − 3)/(3 − 3) = (𝑦 − (−2))/( −2 − (−2)) = (𝑧 − (−5))/(6 − (−5)) (𝒙 − 𝟑)/𝟎 = (𝒚 + 𝟐)/𝟎 = (𝒛 + 𝟓)/𝟏𝟏