`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`

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2=0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2=0.

Let l_1a n dl_2 be the two skew lines. If P ,Q are two distinct points on l_1n dR , S are two distinct points on l_2, then prove that P R cannot be parallel to Q Sdot

Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0a n d2lm+2n l-m n=0.

theta_1 and theta_2 are the inclination of lines L_1 and L_2 with the x-axis. If L_1 and L_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is

Find the direction cosines of the two lines which are connected by the relations l-5m+3n=0 and 7l^(2)+5m^(2)-3n^(2)=0-

Eliminate theta each of the following : l_1cos theta+m_1sin theta+n_1=0,l_2cos theta+m_2sin theta+n_2=0

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

Find the acute angle between the two straight lines whose direction cosines are given by l+m+n=0, l^(2)+m^(2)-n^(2)=0

Let R be the relation over the set of straight lines of a plane such that l_1 R l_2 iff l_1 bot l_2 . Then R is