`L_1a n dL_2` are two lines. If the reflection of `L_1onL_2` and the reflection of `L_2` on `L_1` coincide, then the angle between the lines is (a)`30^0` (b) `60^0` `45^0` (d) `90^0`

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

If the direction ratios l, m ,n of the lines satisfy l-5m+3n=0, 7l^(2)+5m^(2)-3n^(2)=0 then the angle between the lines is

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

If the direction cosines of two lines are connected by the equations l+m+n=0 and l^(2) + m^(2) -n^(2)=0 , then the angle between these lines is of measure

A point P is 3units away from line L_1= 3x + 4y +5=0 and 4 units away from the line L_2 = 8x-by +9=0, The reflection of P on L_1, is P_1 the reflection of P_1 on L_2, is P_2 the reflection of P_3, on L_2, is P_4, Then the area (in sq. units) of figure formed by joining P_1P_2P_3, and P_4, 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