   1. Chapter 10 Class 12 Vector Algebra (Term 2)
2. Serial order wise
3. Ex 10.2

Transcript

Ex 10.2, 18 In triangle ABC (Fig 10.18),which of the following is not true (A) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ + (𝐶𝐴) ⃗= 0 ⃗ (B) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ – (𝐴𝐶) ⃗= 0 ⃗ (C) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ – (𝐶𝐴) ⃗= 0 ⃗ (D) (𝐴𝐵) ⃗ – (𝐶𝐵) ⃗ + (𝐶𝐴) ⃗= 0 ⃗ In Δ ABC, (𝐴𝐶) ⃗ is the resultant of (𝐴𝐵) ⃗ & (𝐵𝐶) ⃗ (𝐴𝐶) ⃗ = (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ = (𝐴𝐶) ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (𝐴𝐶) ⃗ = 0 ⃗ Checking part (A) (𝑨𝑩) ⃗ + (𝑩𝑪) ⃗ + (𝑪𝑨) ⃗= 𝟎 ⃗ From (1) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (𝐴𝐶) ⃗ = 0 ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (−(𝐶𝐴) ⃗) = 0 ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ + (𝐶𝐴) ⃗ = 0 ⃗ Hence, (A) is true. Checking part (B) (𝑨𝑩) ⃗ + (𝑩𝑪) ⃗ – (𝑨𝑪) ⃗= 𝟎 ⃗ From (1) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (𝐴𝐶) ⃗ = 0 ⃗ Hence, (B) is true. Checking part (C) (𝑨𝑩) ⃗ + (𝑩𝑪) ⃗ – (𝑪𝑨) ⃗= 𝟎 ⃗ From (1) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (𝐴𝐶) ⃗ = 0 ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (−(𝐶𝐴) ⃗) = 0 ⃗ (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ + (𝐶𝐴) ⃗ = 0 ⃗ Hence, (C) is not true. Checking part (D) (𝑨𝑩) ⃗ – (𝑪𝑩) ⃗ + (𝑪𝑨) ⃗= 𝟎 ⃗ From (1) (𝐴𝐵) ⃗ + (𝐵𝐶) ⃗ − (𝐴𝐶) ⃗ = 0 ⃗ (AB) ⃗ − (CB) ⃗ + (CA) ⃗ = 0 ⃗ Hence, (D) is true. Thus, (C) is the correct option 