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If the two vectors α3i^+αj^+k^ and 2i^-j^+8k^ are perpendicular to each other, then find the value of α. - Mathematics

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प्रश्न

If the two vectors `3hati + αhatj + hatk` and `2hati - hatj + 8hatk` are perpendicular to each other, then find the value of α.

योग
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उत्तर

`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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