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Example 26 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams

Example 27 (Supplementary NCERT) Deleted for CBSE Board 2025 Exams

Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 29 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 30 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2025 Exams

Last updated at April 16, 2024 by Teachoo

Example 28 Let 𝑎 ⃗, 𝑏 ⃗ and 𝑐 ⃗ be three vectors such that |𝑎 ⃗|= 3, |𝑏 ⃗|= 4, |𝑐 ⃗|= 5 and each one of them being perpendicular to the sum of the other two, find |𝑎 ⃗" + " 𝑏 ⃗" + " 𝑐 ⃗ |.Given, |𝑎 ⃗| = 3 , |𝑏 ⃗| = 4 , |𝑐 ⃗|= 5 Also, Each one of them being perpendicular to the sum of the other two 𝒂 ⃗ is perpendicular to 𝒃 ⃗ + 𝒄 ⃗ 𝑎 ⃗. (𝑏 ⃗ + 𝑐 ⃗) = 0 𝒂 ⃗. 𝒃 ⃗ + 𝒂 ⃗. 𝒄 ⃗ = 0 𝒃 ⃗ is perpendicular to 𝒂 ⃗ + 𝒄 ⃗ 𝑏 ⃗. (𝑎 ⃗ + 𝑐 ⃗) = 0 𝒃 ⃗. 𝒂 ⃗ + 𝒃 ⃗. 𝒄 ⃗ = 0 𝒄 ⃗ is perpendicular to 𝒂 ⃗ + 𝒃 ⃗ 𝑐 ⃗. (𝑎 ⃗ + 𝑏 ⃗) = 0 𝒄 ⃗. 𝒂 ⃗ + 𝒄 ⃗. 𝒃 ⃗ = 0 Now, |𝒂 ⃗+𝒃 ⃗+𝒄 ⃗ |2 = (𝒂 ⃗ + 𝒃 ⃗ + 𝒄 ⃗) . (𝒂 ⃗ + 𝒃 ⃗ + 𝒄 ⃗) = 𝑎 ⃗. 𝑎 ⃗ + 𝑎 ⃗ . 𝑏 ⃗ + 𝑎 ⃗ . 𝑐 ⃗ + 𝑏 ⃗ . 𝑎 ⃗ + 𝑏 ⃗ . 𝑏 ⃗ + 𝑏 ⃗ . 𝑐 ⃗ + 𝑐 ⃗ . 𝑎 ⃗ + 𝑐 ⃗ . 𝑏 ⃗ + 𝑐 ⃗ . 𝑐 ⃗ = 𝑎 ⃗. 𝑎 ⃗ + (𝒂 ⃗ . 𝒃 ⃗ + 𝒂 ⃗ . 𝒄 ⃗) + 𝑏 ⃗ . 𝑏 ⃗ + (𝒃 ⃗ . 𝒂 ⃗ + 𝒃 ⃗ . 𝒄 ⃗) + 𝑐 ⃗ . 𝑐 ⃗ + (𝒄 ⃗ . 𝒂 ⃗ + 𝒄 ⃗ . 𝒃 ⃗ = 𝑎 ⃗. 𝑎 ⃗ + (0) + 𝑏 ⃗ . 𝑏 ⃗ + (0) + 𝑐 ⃗ . 𝑐 ⃗ + (0) = 𝒂 ⃗. 𝒂 ⃗ + 𝑏 ⃗. 𝑏 ⃗ + 𝑐 ⃗. 𝑐 ⃗ = "|" 𝒂 ⃗"|"2 + "|" 𝑏 ⃗"|"2 + "|" 𝑐 ⃗"|"2 = 32 + 42 + 52 = 9 + 16 + 25 = 50 So, |𝒂 ⃗+𝒃 ⃗+𝒄 ⃗ |2 = 50 Taking square root both sides, "|" 𝑎 ⃗ "+ " 𝑏 ⃗" + " 𝑐 ⃗"|" = √50 "|" 𝑎 ⃗ "+ " 𝑏 ⃗ "+ " 𝑐 ⃗"|" = √25 × √2 "|" 𝒂 ⃗ "+ " 𝒃 ⃗ "+ " 𝒄 ⃗"|" = 𝟓√𝟐 = 𝑎 ⃗. 𝑎 ⃗ + (0) + 𝑏 ⃗ . 𝑏 ⃗ + (0) + 𝑐 ⃗ . 𝑐 ⃗ + (0) = 𝒂 ⃗. 𝒂 ⃗ + 𝑏 ⃗. 𝑏 ⃗ + 𝑐 ⃗. 𝑐 ⃗ = "|" 𝒂 ⃗"|"2 + "|" 𝑏 ⃗"|"2 + "|" 𝑐 ⃗"|"2 = 32 + 42 + 52 = 9 + 16 + 25 = 50 So, |𝒂 ⃗+𝒃 ⃗+𝒄 ⃗ |2 = 50 Taking square root both sides, "|" 𝑎 ⃗ "+ " 𝑏 ⃗" + " 𝑐 ⃗"|" = √50 "|" 𝑎 ⃗ "+ " 𝑏 ⃗ "+ " 𝑐 ⃗"|" = √25 × √2 "|" 𝒂 ⃗ "+ " 𝒃 ⃗ "+ " 𝒄 ⃗"|" = 𝟓√𝟐