Let `(l_1,m_1,n_1) and (l_2,m_2,n_2)` be d.c's of two lines.Then the lines are parallel if `l_1/l_2=m_1/m_2=n_1/n_2` (Prove It)

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 te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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=

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

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

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 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

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) The angle between the lines whose direction cosines are (1/2, 1/2,1/sqrt(2)) and (-1/2, -1/2, 1/sqrt(2)) is

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two lines and l , m, n are the direction cosines of a line perpendicular to the given two lines, then

STATEMENT-1 : If a line making an angle pi//4 with x-axis, pi//4 with y-axis then it must be perpendicular to z-axis and STATEMENT-2 : If direction ratios of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) then the angle between them is given by theta = cos ^(-1)(l_(1)l_(2)+m_(2)m_(2)+n_(1)n_(2))