If the angle between line with d.c’s −221,a21,b21 and other line with d.c’s 354,354,−654 is 90°C then a pair of possible values of ‘ a’ and ‘ b’ respectively are

l2+m2+n2=1⇔4+a2+b2=21a2+b2=17.......1Angle between the given lines is 90°⇒−221314+921354+b21−654=0⇒a−2b=2.......2Solve 1&2 we get a=4,b=1

If the angle between line with d.c’s −221,a21,b21 and other line with d.c’s 354,354,−654 is 90°C then a pair of possible values of ‘ a’ and ‘ b’ respectively are

l2+m2+n2=1⇔4+a2+b2=21a2+b2=17.......1Angle between the given lines is 90°⇒−221314+921354+b21−654=0⇒a−2b=2.......2Solve 1&2 we get a=4,b=1

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If the angle between line with d.c’s $(- \frac{2}{\sqrt{21}}, \frac{a}{\sqrt{21}}, \frac{b}{\sqrt{21}})$ and other line with d.c’s $(\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, - \frac{6}{\sqrt{54}})$ is $90 ° C$ then a pair of possible values of ‘ $a$ ’ and ‘ $b$ ’ respectively are

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$4, 1$

$4, 2$

$- 4, - 2$

$- 1, 4$

answer is C.

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Detailed Solution

$l^{2} + m^{2} + n^{2} = 1 \Leftrightarrow 4 + a^{2} + b^{2} = 21$

$a^{2} + b^{2} = 17....... (1)$

Angle between the given lines is $90 °$

$\Rightarrow (\frac{- 2}{\sqrt{21}}) (\frac{3}{\sqrt{14}}) + (\frac{9}{\sqrt{21}}) (\frac{3}{\sqrt{54}}) + (\frac{b}{\sqrt{21}}) (\frac{- 6}{\sqrt{54}}) = 0$

$\Rightarrow a - 2 b = 2....... (2)$

Solve $(1) & (2)$ we get $a = 4, b = 1$

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If the angle between line with d.c’s −221,a21,b21 and other line with d.c’s 354,354,−654 is 90°C then a pair of possible values of ‘ a’ and ‘ b’ respectively are

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If the angle between line with d.c’s $(- \frac{2}{\sqrt{21}}, \frac{a}{\sqrt{21}}, \frac{b}{\sqrt{21}})$ and other line with d.c’s $(\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, - \frac{6}{\sqrt{54}})$ is $90 ° C$ then a pair of possible values of ‘ $a$ ’ and ‘ $b$ ’ respectively are