The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0, l^{2} + m^{2} - n^{2} = 0$ , is given by

\frac{2 π}{3}

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\frac{π}{6}

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\frac{5 π}{3}

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\frac{π}{3}

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Solution

The correct option is D $\frac{π}{3}$
Given, $l + m + n = 0$ ....(i)

$l^{2} + m^{2} - n^{2} = 0$ ....(ii)

Also, $l^{2} + m^{2} + n^{2} = 1$ ....(iii)

On solving equations (i), (ii) and (iii), we get

$m = \pm \frac{1}{\sqrt{2}}, n = \mp \frac{1}{\sqrt{2}}$

and $l = 0$

$∴ θ = \frac{π}{3}$ or $\frac{π}{2}$

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Similar questions

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0, l^{2} + m^{2} - n^{2} = 0$ is given by
[MP PET 1993; RPET 2001]

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The angle between the lines whose direction cosines satisfy the equations l+m+n=0,l2+m2−n2=0, is given by

The correct option is D π3Given, l+m+n=0 ....(i) l2+m2−n2=0 ....(ii)Also, l2+m2+n2=1 ....(iii)On solving equations (i), (ii) and (iii), we getm=±1√2,n=∓1√2 and l=0∴θ=π3 or π2

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0, l^{2} + m^{2} - n^{2} = 0$ , is given by