Ex 10.4, 11 Let the vectors π β and π β be such that |π β| = 3 and |π β| = β2/3, Then π β Γ π β is a unit vector, if the angle between π β and π β is (A) Ο/6 (B) Ο/4 (C) Ο/3 (D) Ο/2 |π β | = 3 & |π β | = β2/3
π β Γ π β = |π β | |π β | sin ΞΈ π Μ
Given, (π β Γ π β) is a unit vector
Magnitude of (π β Γ π β) = |π β Γ π β| = 1
Now,
|π β" Γ " π β | = |(|π β |" " |π β |" sin ΞΈ " π Μ )| , ΞΈ is the angle between π β and π β.
|π β" Γ " π β | = |π β | |π β | sin ΞΈ |π Μ |
|π β" Γ " π β | = |π β | |π β | sin ΞΈ Γ 1
|π β" Γ " π β | = |π β | |π β | sin ΞΈ
1 = 3 Γ β2/3 sin ΞΈ
1 = β2 sinΞΈ
sin ΞΈ = 1/β2
ΞΈ = sin-1 (π/βπ) = π /π
Therefore, the angle between the vectors π β and π β is π /π .
Hence, (B) is the correct option
π Μ ππ π π’πππ‘ π£πππ‘ππ ππππππππππ’πππ π‘π π β πππ π β
ππ,"|" π Μ"|"=1

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.