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If a→,b→,c→ are three vectors such that |a→|=|c→|=1|b→|=4|b→×c→|=22b→=c→+λa→ where λ is a scalar. If the value of λ is equal to α−β3 where α and β are natural numbers, then find the value of α+β

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answer is 73.

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Detailed Solution

Given |b→×c→|=2|b→||c→|sin⁡θ=2⇒sin⁡θ=12θ=30∘ Hence, angle between b→ and c¯ is 30∘. Now, 2b→−c→=λa→⇒|2b→−c→|=|λa→|⇒|2b→−c→|2=λ2|a→|2 Hene, λ2=65−83λ=65−83≡α−β3 Hence, α=65 and β=8α+β=73

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If a→,b→,c→ are three vectors such that |a→|=|c→|=1|b→|=4|b→×c→|=22b→=c→+λa→ where λ is a scalar. If the value of λ is equal to α−β3 where α and β are natural numbers, then find the value of α+β