Let a → = α i ^ + 3 j ^ - k ^ , b → = 3 i ^ - β j ^ + 4 k ^ and c → = i ^ + 2 j…

Let a→=αi^+3j^-k^,b→=3i^-βj^+4k^ and c→=i^+2j^-2k^ where α,β∈R be three vectors. If the projection of a→ on c→ is 103 andb→×c→=-6i^+10j^+7k^ , then the value of α+β equal to
  1. 3
  2. 4
  3. 5
  4. 6

Solution

Given a→=αi^+3j^-k^,b→=3i^-βj^+4k^ and c→=i^+2j^-2k^ where α,β∈R be three vectors.

Projection of a→ on c→ is a→·c→c→=103 (given)

⇒α+6+21+4+4=103⇒α=2

and b→×c→=i^j^k^3-β412-2=-6i^+j^+k^

⇒2β-8=-6⇒β=1

Hence α+β=3

Asked in: JEE Main 2022 (29 Jun Shift 1)

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