Ex 10.3

Ex 10.3, 1

Ex 10.3, 2

Ex 10.3, 3 Important

Ex 10.3, 4

Ex 10.3, 5 Important

Ex 10.3, 6

Ex 10.3, 7

Ex 10.3, 8

Ex 10.3, 9 Important

Ex 10.3, 10 Important You are here

Ex 10.3, 11

Ex 10.3, 12 Important

Ex 10.3, 13 Important

Ex 10.3, 14

Ex 10.3, 15 Important

Ex 10.3, 16 Important

Ex 10.3, 17

Ex 10.3, 18 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 10.3, 10 If 𝑎 ⃗ = 2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = −𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂ and 𝑐 ⃗ = 3𝑖 ̂ + 𝑗 ̂ are such that 𝑎 ⃗ +𝜆𝑏 ⃗ is perpendicular to 𝑐 ⃗ , then find the value of 𝜆.𝑎 ⃗ = 2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂ 𝑏 ⃗ = −𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂ = −1𝑖 ̂ + 2𝑗 ̂ + 1𝑘 ̂ 𝑐 ⃗ = 3𝑖 ̂ + 𝑗 ̂ = 3𝑖 ̂ + 1𝑗 ̂ + 0𝑘 ̂ Now, (𝑎 ⃗ + 𝜆𝑏 ⃗) = (2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂) + 𝜆 (-1𝑖 ̂ + 2𝑗 ̂ + 1𝑘 ̂) = 2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂ − 𝜆𝑖 ̂ + 2𝜆𝑗 ̂ + 𝜆𝑘 ̂ = (2 − 𝜆) 𝑖 ̂ + (2 + 2𝜆) 𝑗 ̂ + (3 + 𝜆) 𝑘 ̂ Since (𝑎 ⃗ + 𝜆𝑏 ⃗) is perpendicular to 𝑐 ⃗ (𝑎 ⃗ + 𝜆𝑏 ⃗). 𝑐 ⃗ = 0 [(2−𝜆) 𝑖 ̂+(2+2𝜆) 𝑗 ̂+(3+𝜆)𝑘 ̂ ] . (3𝑖 ̂ + 1𝑗 ̂ + 0𝑘 ̂) = 0 (2 − 𝜆).3 + (2 + 2𝜆).1 + (3 + 𝜆 ).0 = 0 3.2 − 3𝜆 + 2 + 2𝜆 + 0 = 0 6 – 3𝜆 + 2 + 2𝜆 = 0 8 − 𝜆 = 0 𝜆 = 8 ∴ 𝜆 = 8 (Dot product of perpendicular vectors is 0)