मराठी

If a→=i^-j^+7k^ and λb→=5i^-j^+λk^, then find the value of λ so that the vectors a→+b→ and a→-b→ are orthogonal. - Mathematics

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प्रश्न

If `veca = hati - hatj + 7hatk` and `vecb = 5hati - hatj + λhatk`, then find the value of λ so that the vectors `veca + vecb` and `veca - vecb` are orthogonal.

बेरीज
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उत्तर

`veca = hati - hatj + 7hatk` and `vecb = 5hati - hatj + λhatk`

Hence `veca + vecb = 6hati - 2hatj + (7 + λ)hatk` and `veca - vecb = - 4hati + (7 - λ)hatk`

`veca + vecb` and `veca - vecb` will be orthogonal if, `(veca + vecb).(veca - vecb)` = 0

i.e., if, – 24 + (49 – λ2) = 0

⇒ λ2 = 25

i.e., if, λ = ±5

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