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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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