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Question
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.
Solution
`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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