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`

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

The line l_1 x+ m_1 y+n=0 and l_2 x + m_2 y+n=0 will cut the coordinate axes at concyclic points if (A) l_1 m_1 = l_2 m_2 (B) l_1 m_2 = l_2 m_1 (C) l_1 l_2 = m_1 m_2 (D) l_1 l_2 m_1 m_2 = n^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

If three mutually perpendicular lines have direction cosines (l_1,m_1,n_1),(l_2,m_2,n_2) and (l_3 ,m_3, n_3) , then the line having direction ratio l_1+l_2+l_3,m_1+ m_2+m_3, and n_1 + n_2 + n_3 , make an angle of

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

Assertion: The lines x/1=y/2=z/3 and (x-1)/(-2)=(y-2)/(-4)=(z-3)/(-6) are parallel., Reason: two lines having direction ratios l_1,m_1,n_1 and l_2,m_2,n_2 are parallel if l_1/l_2=m_1/m_2=n_1/n_2 . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 are proportional to l_1+l_2,m_1+m_2, n_1+n_2dot Statement 2: The angle between the two intersection lines having direction cosines as l_1,m_1, n_1a n dl_2, m_2, n_2 is given by costheta=l_1l_2+m_1m_2+n_1n_2dot

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If l_1^2+m_1^2+n_1^2=1 etc., and l_1 l_2+m_1 m_2+n_1 n_2 = 0 , etc. and Delta=|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)| then

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If l_(1)=1/sqrt(3), m_(1)=1/sqrt(3) then the value of n_(1) is equal to