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Example 13 - Find angle between vectors  a and b, magnitudes

Example 13 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 13 Find the angle between two vectors π‘Ž βƒ— and 𝑏 βƒ— with magnitudes 1 and 2 respectively and when π‘Ž βƒ— ⋅𝑏 βƒ— =1. "Given |" 𝒂 βƒ—"| = 1 , |" 𝒃 βƒ—"| = 2 , " "and " 𝒂 βƒ—". " 𝒃 βƒ—" = 1" We know that 𝒂 βƒ— . 𝒃 βƒ— = "|" 𝒂 βƒ—"|" "|" 𝒃 βƒ—"|" cos ΞΈ where ΞΈ is the angle between π‘Ž βƒ— and 𝑏 βƒ— Putting values in formula π‘Ž βƒ— . 𝑏 βƒ— = "|" π‘Ž βƒ—"|" "|" 𝑏 βƒ—"|" cos ΞΈ 1 = 1 Γ— 2 Γ— cos ΞΈ cos ΞΈ = 1/2 cos ΞΈ = cos 𝝅/πŸ‘ So, ΞΈ = 𝝅/πŸ‘ Thus angle b/w π‘Ž βƒ— and 𝑏 βƒ— is πœ‹/3 .

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