If the direction ratio of two lines are given by `3lm-4ln+mn=0 and l+2m+3n=0`, then the angle between the lines, is

The dr's of two lines are given by a+b+c=0,2ab +2ac-bc=0 . Then the angle between the lines is

The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

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))

The direction cosines of two lines satisfy 2l+2m-n=0 and lm+mn+nl=0 . The angle between these lines is

The direction cosines of two lines are given by the equations 3m+n+5l=0, 6nl-2lm+5mn=0. find the angle between them

If the direction cosines of two lines given by the equations p m+qn+rl=0 and lm+mn+nl=0 , prove that the lines are parallel if p^2+q^2+r^2=2(pq+qr+rp) and perpendicular if pq+qr+rp=0

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) 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

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

The direction cosines of two lines are connected by relation l+m+n=0 and 4l is the harmonic mean between m and n. Then,