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If \( l_1, m_1, n_1 \: and \: l_2, m_2, n_2 \) are direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are \( m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1.\)
cbse
class12
modelpaper
2012
sec-c
q27
math
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asked
Jan 4, 2013
by
thanvigandhi_1
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0
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If $l_1,m_1,n_1,l_2,m_2,n_2,l_3,m_3,n_3$ are direction cosines of three mutually perpendicular lines,prove that the line whose direction cosines are proportional to $l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3$ make equal angles with them.
asked
Jan 4, 2013
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If $ l_1, m_1, n_1$ and $l _2, m_2, n_2 $ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are $m_1n_2-m_2n_1$, $n_1l_2-n_2l_1$, $l_1m_2-l_2m_1$
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Nov 2, 2012
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The direction cosine of a line which is $\perp$ to two perpendicular lines whose direction cosines are $(l_1,m_1,n_1)\:\:and\:\:(l_2,m_2,n_2)$ is ?
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Jan 8, 2014
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Let L be the set of all lines in a plane and R be thr relation in L defined as \( \{(L_1, L_2):L_1\) is perpendicular to \( L_2 \}. \) Show that R is symmetric but neither reflexive nor transitive.
asked
Jan 30, 2013
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Let L be the set of all lines in XY - planes and R be the relation in L defined as R = \( { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} \). Show the R is an equivalence relation. Find the set of all the lines related to the line \( y=2x+4.\)
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Jan 11, 2013
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Find the vector equation of the line through the point ( 1, 2, -4 ) and perpendicular to the two lines $\large \frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7} $ and, $ \large\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5} $
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Jan 3, 2013
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thanvigandhi_1
cbse
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Show that the line joining the origin to the point (2, 1, 1) is perpendicular the line determined by the point (3, 5, -1),(4, 3, -1).
asked
Jan 8, 2013
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-c
q27
math
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