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Ex 10.3, 8 - Find magnitude of two vectors a, b, having same

Ex 10.3, 8 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.3, 8 Find the magnitude of two vectors π‘Ž βƒ— and 𝑏 βƒ—, having the same magnitude and such that the angle between them is 60Β° and their scalar product is 1/2 . Given, magnitude of two vectors π‘Ž βƒ— and 𝑏 βƒ— is same So, |π‘Ž βƒ— | = |𝑏 βƒ— | We know that , π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— | |𝑏 βƒ— | cos ΞΈ , ΞΈ is the angle between π‘Ž βƒ— and 𝑏 βƒ— Given ΞΈ = 60Β° & π‘Ž βƒ— . 𝑏 βƒ— = 1/2 Now, π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— | |𝑏 βƒ— | cos ΞΈ π‘Ž βƒ— . 𝑏 βƒ— = |π‘Ž βƒ— | |π‘Ž βƒ— | cos 60Β° 1/2 = |π‘Ž βƒ— |2 Γ— 1/2 |π‘Ž βƒ— |2 = 1 |π‘Ž βƒ— | = Β± 1 Since, magnitude of a vector is not negative, So, |π‘Ž βƒ— | = 1 So |𝒂 βƒ— | = |𝒃 βƒ— | = 1 Thus, magnitude of π‘Ž βƒ— and 𝑏 βƒ— is 1.

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