Home
Class 12
MATHS
Prove that the three lines drown from or...

Prove that the three lines drown from origin with direction cosines `(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3)` are coplanar if `[[l_1,m_1,n_1],[l_2,m_2,n_2],[l_3,m_3,n_3]]=0.`

Text Solution

Verified by Experts

Let ` oversettoa=l_1i+m_1j+n_1koversettobl_2i+m_2j+n_2koversettocl_3i+m_3j+n_3k` The lines co-planar if `oversettoa.(oversettobxxoversettoc)=0iff|(l_1,m_1,n_1),(l_2,m_2,n_2),(l_3,m_3,n_3):|=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the acute angle between the lines whose direction cosines are given by the relation l+ m+n=0 and l^2+m^2-n^2=0 and pi/3

Prove that the two lines whose direction cosines are connected by the equations l+2m+3n=0, 3lm-4ln+mn=0 are perpendicular to each other.

Write the possible values of l and m for an electron in 3rd orbital.

Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) are equal.