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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  3-D Geometry
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Q)

The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?

$(a)\:\:0\:\:\:\qquad\:\:(b)\:\:30^{\circ}\:\:\:\qquad\:\:(c)\:\:60^{\circ}\:\:\:\qquad\:\:(d)\:\:90^{\circ}$

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A)
The eqn. of the lines are $x=1,\:\:y=2$.....(i) and $y=-1,\:\:z=0$.....(ii)
The equations can be written as
$\large\frac{x-1}{0}=\frac{y-2}{0}=\frac{z}{1}=\lambda$.........(i) and
$\large\frac{x}{1}=\frac{y+1}{0}=\frac{z}{0}=\mu$.........(ii)
$\therefore$ The $d.r.$ of the lines are $(0,0,1)\:\:and\:\:(1,0,0)$
Angle between them is given by $cos\theta=\large\frac{(0,0,1).(1,0,0)}{\sqrt 1.\sqrt 1}$$=0$
$\therefore$ $\theta=90^{\circ}$
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