`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` (c)`45^0` (d) `90^0`

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,

theta_1 and theta_2 are the inclination of lines L_1a n dL_2 with the x-axis. If L_1a n dL_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is (a) (x-x_1)/(cos((theta_1+theta_2)/2))=(y-y_1)/(sin((theta_1+theta_2)/2)) (b) (x-x_1)/(-sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2)) (c) (x-x_1)/(sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2)) (d) (x-x_1)/(-sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2))

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

Line l is parallel to line m. It slopes of line l is 1/2 then slope of line m is ________

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.

If line l_1 is perpendicular to line l_2 and line l_3 has slope 3 then find the equation of line l_1

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is (a) 500 (b) 450 (c) 230 (d) 465

P_1n dP_2 are planes passing through origin L_1a n dL_2 are two lines on P_1a n dP_2, respectively, such that their intersection is the origin. Show that there exist points A ,Ba n dC , whose permutation A^(prime),B^(prime)a n dC^(prime), respectively, can be chosen such that A is on L_1,BonP_1 but not on L_1a n dC not on P_1; A ' is on L_2,B 'onP_2 but not on L_2a n dC ' not on P_2dot

If line l_1 is perpendicular to line l_2 and line l_3 has slope 3 then find the equation of line l_2

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_2 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_2 (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (a) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.