Range

JEE Mains 2015 Online › 3D and Vectors questions › Range

unit vectors a and b are perpendicular to each other and unit vector c is inclined at angle Î¸ to both a and b.If c=m(a+b)+n(axb) and m,n are real.Find range of Î¸

I have found m=cosÎ¸...and nothing else..help me out

#Mathematics #3D and Vectors

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3 Answers

Lokesh Verma ·2009-11-12 23:14:16

minimum will be 45 and maximum will be 135 ?

Think in terms of pure geometry..

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eureka123 ·2009-11-12 23:44:46

ya it is...but how to do it properly ??

i mean vector method...

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Lokesh Verma ·2009-11-12 23:48:54

|c| = √m²+m²+n²

Take dot product of c with a....
Now can you finish it??

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Basic Integral Calculus Operators Symbols Matrix Cases

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∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

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+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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Range

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