lines `L_1:ax+by+c=0` and `L_2:lx+my+n=0` intersect at the point `P` and make a angle `theta` between each other. find the equation of a line `L`different from `L_2` which passes through `P` and makes the same angle `theta` with `L_1`

Lines L_(1)-=ax+by+c=0 and L_(2)-=lx+my+n=0 intersect at the point P and make an angle theta with each other.Find the equation of a line theta different from L_(2) .Find passes through of a line different from L_(2) whic theta with L_(1).

Lines, L_1 :x + sqrt3y=2, and L_2 : ax+by=1 meet at P and enclose an angle of 45° between them. Line L_3 : y=sqrt3x also passes through P then -

If L_1 and L_2, are two lines belonging to family of lines (3 + 2lambda) x+(4 + 3lambda) y-7-5lambda =0 (lambda is parameter) such that it is at maximum and miimum distance from (2, 3), respectively, then theequation of lines passing through (1, 2) and making equal angles with L_1 and L_2 is/are

Lines,L_(1):x+sqrt(13y)=2, and L_(2):ax+by=1 meet at P and enclose an angle of 45^(@) betweenthem.Line L_(3):y=sqrt(13x), also passes through P then

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

if line 2x+7y-1=0 intersect the lines L1:3x+4y+1=0 and L2:6x+8y-3=0 in A and B respectively,then equation of line parallal to L1 and L2 and passes through a point P such that AP:PB=2:1 (internally) is (P is on the line 2x + 7y-1=0)

If the length of the perpendicular to a line L from the origin is 8 and the perpendicular makes an angle of 60^(@) with the X-axis then the equation of line L is

Two lines l and m interset at the O and P is Point on a line n Passing through the point O such that P is equidistant from l and m. Prove that n is the bisectof the angle formed by l and m