
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 10.3
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 May 29, 2023 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)