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Ex 10.4, 11 - Let |a|= 3, |b| = root2/3, Then a x b is unit vector

Ex 10.4, 11 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.4, 11 Let the vectors π‘Ž βƒ— and 𝑏 βƒ— be such that |π‘Ž βƒ—| = 3 and |𝑏 βƒ—| = √2/3, Then π‘Ž βƒ— Γ— 𝑏 βƒ— is a unit vector, if the angle between π‘Ž βƒ— and 𝑏 βƒ— is (A) Ο€/6 (B) Ο€/4 (C) Ο€/3 (D) Ο€/2 |π‘Ž βƒ— | = 3 & |𝑏 βƒ— | = √2/3 π‘Ž βƒ— Γ— 𝑏 βƒ— = |π‘Ž βƒ— | |𝑏 βƒ— | sin ΞΈ 𝑛 Μ‚ Given, (π‘Ž βƒ— Γ— 𝑏 βƒ—) is a unit vector Magnitude of (π‘Ž βƒ— Γ— 𝑏 βƒ—) = |𝒂 βƒ— Γ— 𝒃 βƒ—| = 1 Now, |𝒂 βƒ—" Γ— " 𝒃 βƒ— | = |(|𝒂 βƒ— |" " |𝒃 βƒ— |" sin ΞΈ " 𝒏 Μ‚ )| , ΞΈ is the angle between π‘Ž βƒ— and 𝑏 βƒ—. |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = |π‘Ž βƒ— | |𝑏 βƒ— | sin ΞΈ |𝑛 Μ‚ | |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = |π‘Ž βƒ— | |𝑏 βƒ— | sin ΞΈ Γ— 1 |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = |π‘Ž βƒ— | |𝑏 βƒ— | sin ΞΈ 1 = 3 Γ— √2/3 sin ΞΈ 1 = √2 sinΞΈ sin ΞΈ = 1/√2 ΞΈ = sin-1 (𝟏/√𝟐) = 𝝅/πŸ’ Therefore, the angle between the vectors π‘Ž βƒ— and 𝑏 βƒ— is 𝝅/πŸ’ . Hence, (B) is the correct option 𝑛 Μ‚ 𝑖𝑠 π‘Ž 𝑒𝑛𝑖𝑑 π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘π‘’π‘Ÿπ‘π‘’π‘›π‘‘π‘–π‘π‘’π‘™π‘Žπ‘Ÿ π‘‘π‘œ π‘Ž βƒ— π‘Žπ‘›π‘‘ 𝑏 βƒ— π‘†π‘œ,"|" 𝑛 Μ‚"|"=1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.