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The angle between two straight lines having direction cosines $〈\frac{l}{\sqrt{21}}, \frac{m}{\sqrt{21}}, \frac{1}{\sqrt{21}}〉 and 〈\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, \frac{3 l}{\sqrt{54}}〉$ is $90^{0}$ , then a pair of possible values of $l, m$ respectively are

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Correct option is B

If the direction ratios of two perpendicular lines are proportional to a1,b1,c1,a2,b2,c2 then a1a2+b1b2+c1c2=0Hence l21⋅354+m21⋅354+121⋅3l54=0It implies that 6l+3m=0⇒2l+m=0Verify the options for suitable values of l,m

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The angle between two straight lines having direction cosines l21,m21,121 and 354,354,3l54 is 900, then a pair of possible values of l,m respectively are

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The angle between two straight lines having direction cosines $〈\frac{l}{\sqrt{21}}, \frac{m}{\sqrt{21}}, \frac{1}{\sqrt{21}}〉 and 〈\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, \frac{3 l}{\sqrt{54}}〉$ is $90^{0}$ , then a pair of possible values of $l, m$ respectively are