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Question
Choose correct alternatives:
If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.
Options
`(11)/(4)`
`-(11)/(4)`
`(11)/(2)`
`(4)/(11)`
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Solution
If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is `\underline(-(11)/(4))`.
Eplanation:
`x/3 = y/4 = z => (3,4,1)`
`(x-1)/k = (y+2)/3 = (z-3)/(k-1) = (k, 3, k-1)`
(3, 4, 1) × (k, 3, k − 1) = 0
3k + 4 ⋅ 3 + 1 ⋅ (k − 1) = 0
3k + 12 + k − 1 = 0
4k + 11 = 0 ⇒ k
= `(-11)/4`
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