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Ex 10.4, 6 - Given a.b = 0 and a x b = 0. What are vectors a and b

Ex 10.4, 6 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.4, 6 Given that π‘Ž βƒ— . 𝑏 βƒ— = 0 and π‘Ž βƒ— Γ— 𝑏 βƒ— = 0 βƒ— . What can you conclude about the vectors π‘Ž βƒ— and 𝑏 βƒ— ? 𝒂 βƒ— . 𝒃 βƒ— = 0 π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ β‡’ |π‘Ž βƒ— ||𝑏 βƒ— | cos ΞΈ = 0 β‡’ |π‘Ž βƒ— | = 0 or |𝑏 βƒ— | = 0 or cos ΞΈ = 0 i.e. ΞΈ = 90Β° 𝒂 βƒ— Γ— 𝒃 βƒ— = 0 π‘Ž βƒ— Γ— 𝑏 βƒ— = |π‘Ž βƒ— ||𝑏 βƒ— | sin ΞΈ 𝑛 Μ‚ β‡’ |π‘Ž βƒ— ||𝑏 βƒ— | sinΞΈ 𝑛 Μ‚ = 0 βƒ— β‡’ |π‘Ž βƒ— | = 0 or |𝑏 βƒ— | = 0 or sin ΞΈ = 0 i.e. ΞΈ = 0Β° Given, Since ΞΈ = cannot be equal to 0Β° and 90Β° simultaneously, So, sin ΞΈ = 0 or cos ΞΈ = 0 is not possible. Thus, either |𝒂 βƒ— | = 0 or |𝒃 βƒ— | = 0 Hence, either π‘Ž βƒ— = 0 βƒ— or 𝑏 βƒ— = 0 βƒ— .

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