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If the direction ratios of two perpendicular straight lines are given by $(1, θ, θ^{3} - θ + 7) and (0, 4, θ) where θ \neq 0$ , then ${Tan}^{- 1} (\frac{θ - θ^{3}}{11}) =$

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Correct option is C

The lines having direction ratios a1,b1,c1and a2,b2,c2are perpendicular then a1a2+b1b2+c1c2=0Hence,4θ+θ4−θ2+7θ=0θ3−θ+11=0θ−θ311=1Therefore, Tan−1θ−θ311=π4

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If the direction ratios of two perpendicular straight lines are given by 1,θ,θ3−θ+7 and 0,4,θ where θ≠0, thenTan−1θ−θ311=

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Ready to Test Your Skills?

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If the direction ratios of two perpendicular straight lines are given by $(1, θ, θ^{3} - θ + 7) and (0, 4, θ) where θ \neq 0$ , then ${Tan}^{- 1} (\frac{θ - θ^{3}}{11}) =$