Show that if the axes are rectangular the equation of line through point `(x_1,y_1,z_1)` at right angle to the lines `x/l_1=y/m_1=z/n_1,x/l_2=y/m_2=z/n_2` is `(x-x_1)/(m_1n_2-m_2n_1)=(y-y_1)/(n_1l_2-n_2l_1)=(z-z_1)/(l_1m_2-l_2m_1)`

Show that if the axes are rectangular,the equation of the line through the point (x_(1),y_(1),z_(1)) at right angle to the lines (x)/(l_(1))=(y)/(m_(1))=(z)/(n_(1));(x)/(l_(2))=(y)/(m_(2))=(z)/(n_(2)) is (x-x_(1))/(m_(1)n_(2)-m_(2)n_(1))=(y-y_(1))/(n_(1)l_(2)-n_(2)l_(1))=(z-z_(1))/(l_(1)m_(2)-l_(2)m_(1))

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

If (x-1)/(l)=(y-2)/(m)=(z+1)/(n) is the equation of the line through (1,2,-1) and (-1,0,1) then (l,m,n)

Find the equation of the plane through the line (x)/(l)=(y)/(m)=(z)/(n) and perpendicular to the plane containing the line (x)/(m)=(y)/(n)=(z)/(l) and (x)/(n)=(y)/(l)=(z)/(m)

Two lines with direction cosines l_1,m_1,n_1 and l_2,m_2,n_2 are at righat angles iff (A) l_1l_2+m_1m_2+n_1n_2=0 (B) l_1=l_2,m_1=m_2,n_1=n_2 (C) l_1/l_2=m_1/m_2=n_1/n_2 (D) l_1l_2=m_1m_2=n_1n_2

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

The direction cosines of a line bisecting the angle between two perpendicular lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (1)(l_1+l_2)/2,(m_1+m_2)/2,(n_1+n_2)/2 (2)l_1+l_2,m_1+m_2,n_1+n_2 (3)(l_1+l_2)/(sqrt(2)),(m_1-m_2)/2,(n_1+n_2)/(sqrt(2)) (4)l_1-l_2,m_1-m_2,n_1-n_2 (5)"n o n eo ft h e s e"

(log x)/(l+m-2n)=(log y)/(m+n-2l)=(log z)/(n+l-2m)