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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  3-D Geometry
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The angle between the line formed by $3x-7y-5z=1$ and $8x-11y+2z=0$ and the line formed by $5x-13y+3z+2=0$ and $8x-11y+2z=0$


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Given equations of the planes be
Let the $d.r.$ of the line formed by $ (i)$ and $ (ii)$, $L_1$ be $(l_1,m_2,n_2)$ and
let the $d.r.$ of the line formed by $(ii)$ and $ (iii)$, $L_2$ be $(l_2,m_2,n_2)$
$\Rightarrow\:$ $(l_1,m_1,n_1)\:\:is\:\:\perp$ to $(3,-7,-5)$ and $(8,-11,2)$
$\Rightarrow\: (l_1,m_1,n_1)=(3,-7,-5)\times(8,-11,2)=(-69,-46,23)=(-3,-2,1)$
Similarly $(l_2,m_2,n_2)\:\:is\:\perp$ to $(5,-13,3)\:\:and\:\:(8,-11,2)$
$\therefore$ The angle between $L_1$ and $L_2$ is given by
$=\large\frac{(-3,-2,1).(1,2,7)}{\sqrt {14}.\sqrt { 54}}$$=0$
$\therefore$ $\theta=\large\frac{\pi}{2}$
answered Jan 9, 2014 by rvidyagovindarajan_1

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