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Question
If the two vectors `3hati + αhatj + hatk` and `2hati - hatj + 8hatk` are perpendicular to each other, then find the value of α.
Solution
`veca = 3hati + αhatj + hatk`
and `vecb = 2hati - hatj + 8hatk`
∵ `veca` and `vecb` are perpendicular.
∴ `veca*vecb` = 0
(3)(2) + α(–1) + 1 × 8 = 0
6 – α + 8 = 0
`\implies` α = 14
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