Ex 10.2

Ex 10.2, 1

Ex 10.2, 2

Ex 10.2, 3 Important

Ex 10.2, 4

Ex 10.2, 5 Important

Ex 10.2, 6

Ex 10.2, 7 Important

Ex 10.2, 8 You are here

Ex 10.2, 9

Ex 10.2, 10 Important

Ex 10.2, 11 Important

Ex 10.2, 12

Ex 10.2, 13 Important

Ex 10.2, 14

Ex 10.2, 15 Important

Ex 10.2, 16

Ex 10.2, 17 Important

Ex 10.2, 18 (MCQ) Important

Ex 10.2, 19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 10.2, 8 Find the unit vector in the direction of vector (𝑃𝑄) ⃗ , where P and Q are the points (1, 2, 3) and (4, 5, 6); respectively.P (1, 2, 3) Q (4, 5, 6) (𝑃𝑄) ⃗ = (4 – 1) 𝑖 ̂ + (5 – 2) 𝑗 ̂ + (6 – 3) 𝑘 ̂ = 3𝑖 ̂ + 3𝑗 ̂ + 3𝑘 ̂ ∴ Vector joining P and Q is given by (𝑃𝑄) ⃗ = 3𝑖 ̂ + 3𝑗 ̂ + 3𝑘 ̂ Magnitude of (𝑃𝑄) ⃗ = √(32+32+32) |(𝑃𝑄) ⃗ | = √(9+9+9) = √27 = 3√3 Unit vector in direction of (𝑃𝑄) ⃗ = 1/(𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 (𝑃𝑄) ⃗ ) ×(𝑃𝑄) ⃗ = 1/(3√3) ["3" i ̂" + 3" j ̂" + 3" k ̂ ] = 3/(3√3) 𝑖 ̂ + 3/(3√3) 𝑗 ̂ + 3/(3√3) 𝑘 ̂ = 𝟏/√𝟑 𝒊 ̂ + 𝟏/√𝟑 𝒋 ̂ + 𝟏/√𝟑 𝒌 ̂ Thus, unit vector in direction of (𝑃𝑄) ⃗ = 1/√3 𝑖 ̂ + 1/√3 𝑗 ̂ + 1/√3 𝑘 ̂