Question 10 - If |𝑎⃗| = 3, |𝑏⃗⃗| = 4 and |𝑎⃗ +𝑏⃗⃗| =5, then |a-b|

Question 10 If |𝑎 ⃗|=3,|𝑏 ⃗|=4 and |𝑎 ⃗+𝑏 ⃗|=5, then |𝑎 ⃗−𝑏 ⃗|= (A) 3 (B) 4 (C) 5 (D) 8 Given |𝑎 ⃗|=3,|𝑏 ⃗|=4 and |𝑎 ⃗+𝑏 ⃗ |=5 We need to find |𝑎 ⃗−𝑏 ⃗ | Taking square, |𝒂 ⃗−𝒃 ⃗ |2 = (𝒂 ⃗−𝒃 ⃗). (𝒂 ⃗−𝒃 ⃗) = 𝑎 ⃗ . 𝑎 ⃗ − 𝑎 ⃗ . 𝑏 ⃗ − 𝒃 ⃗. 𝒂 ⃗ + 𝑏 ⃗ . 𝑏 ⃗ = 𝑎 ⃗ . 𝑎 ⃗ − 𝑎 ⃗ . 𝑏 ⃗ − 𝒂 ⃗ . 𝒃 ⃗ + 𝑏 ⃗ . 𝑏 ⃗ = 𝒂 ⃗. 𝒂 ⃗ − 2𝑎 ⃗ . 𝑏 ⃗ + 𝒃 ⃗. 𝒃 ⃗ = |𝒂 ⃗ |2 − 2𝑎 ⃗. 𝑏 ⃗ + |𝒃 ⃗ |2 So, the correct answer is (C) Similarly, |𝒂 ⃗+𝒃 ⃗ |2 = |𝑎 ⃗ |2 + 2𝑎 ⃗. 𝑏 ⃗ + |𝑏 ⃗ |2 Thus, |𝒂 ⃗−𝒃 ⃗ |2 + |𝒂 ⃗+𝒃 ⃗ |2 = |𝑎 ⃗ |2 − 2𝑎 ⃗. 𝑏 ⃗ + |𝑏 ⃗ |2 + |𝑎 ⃗ |2 + 2𝑎 ⃗. 𝑏 ⃗ + |𝑏 ⃗ |2 |𝑎 ⃗−𝑏 ⃗ |2 + |𝑎 ⃗+𝑏 ⃗ |2 = |𝑎 ⃗ |2 + |𝑏 ⃗ |2 + |𝑎 ⃗ |2 + |𝑏 ⃗ |2 |𝒂 ⃗−𝒃 ⃗ |2 + |𝒂 ⃗+𝒃 ⃗ |2 = 2|𝒂 ⃗ |2 + 2|𝒃 ⃗ |2 Putting |𝑎 ⃗|=3,|𝑏 ⃗|=4 and |𝑎 ⃗+𝑏 ⃗ |=5 |𝑎 ⃗−𝑏 ⃗ |2 + 52 = 2 × 32 + 2 × 42 |𝑎 ⃗−𝑏 ⃗ |2 + 25 = 2 × 9 + 2 × 16 |𝑎 ⃗−𝑏 ⃗ |2 = 18 + 32 − 25 |𝑎 ⃗−𝑏 ⃗ |2 = 25 |𝑎 ⃗−𝑏 ⃗ |2 = 52 Square rooting |𝒂 ⃗−𝒃 ⃗ | = 5 So, the correct answer is (C)

Question 10 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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