If `l_1,m_1,n_1` and `l_2,m_2,n_2` are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are `m_1n_2 - m_2n_1, n_1l_2 -n_2l_1, l_1m_2 -l_2m_1`

If 1/2, 1/3, n are the direction cosines of a line , then the values of n is

If 1/2,1/3,n are the direction cosines of a line , then the value of n is

The direction cosines of a line equally inclined to three mutually perpendiclar lines having direction cosines as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3), m_(3),n_(3) are

The direction cosines of a line satisfy the relations lambda(l+m)=n and m n+n l+l m=0. The value of lambda, for which the two lines are perpendicular to each other, is

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,

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

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.

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

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.