Home
Class 12
MATHS
The direction cosines of a line bisectin...

The direction cosines of a line bisecting the angle between two perpendicular lines whose direction cosines are `l_1,m_1,n_1` and `l_2,m_2,n_2` are `(1)(l_1+l_2)/2,(m_1+m_2)/2,(n_1+n_2)/2` `(2)l_1+l_2,m_1+m_2,n_1+n_2` `(3)(l_1+l_2)/(sqrt(2)),(m_1-m_2)/2,(n_1+n_2)/(sqrt(2))` `(4)l_1-l_2,m_1-m_2,n_1-n_2` `(5)"n o n eo ft h e s e"`

Answer

Step by step text solution for The direction cosines of a line bisecting the angle between two perpendicular lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (1)(l_1+l_2)/2,(m_1+m_2)/2,(n_1+n_2)/2 (2)l_1+l_2,m_1+m_2,n_1+n_2 (3)(l_1+l_2)/(sqrt(2)),(m_1-m_2)/2,(n_1+n_2)/(sqrt(2)) (4)l_1-l_2,m_1-m_2,n_1-n_2 (5)"n o n eo ft h e s e" by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

The direction cosines of the lines bisecting the angle between the lines 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

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

Knowledge Check

  • 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

    A
    `(l_1+l_2)/(2sin((theta)/(2))), (m_1+m_2)/(2sin((theta)/(2))), (n_1+n_2)/(2sin((theta)/(2)))`
    B
    `(l_1+l_2)/(2cos((theta)/(2))), (m_1+m_2)/(2cos((theta)/(2))), (n_1+n_2)/(2cos((theta)/(2)))`
    C
    `(l_1-l_2)/(2sin((theta)/(2))), (m_1-m_2)/(2sin((theta)/(2))), (n_1-n_2)/(2sin((theta)/(2)))`
    D
    `(l_1-l_2)/(2cos((theta)/(2))), (m_1-m_2)/(2cos((theta)/(2))), (n_1-n_2)/(2cos((theta)/(2)))`

  • 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

    A
    `l_(1)+l_(2)+l_(3), m_(1)+m_(2)+m_(3), n_(1)+n_(2)+n_(3)`
    B
    `(l_(1)+l_(2)+l_(3))/sqrt(3), (m_(1)+m_(2)+m_(3))/sqrt(3), (n_(1)+n_(2)+n_(3))/sqrt(3)`
    C
    `(l_(1)+l_(2)+l_(3))/3 ,(m_(1)+m_(2)+m_(3))/(3), (n_(1)+n_(2)+n_(3))/(3)`
    D
    none of these

  • The angle between the lines whose direction cosines are given by l+m+n=0 and l^(2)+ m^(2) - n^(2) = 0 is

    A
    `(pi)/(6)`
    B
    `(pi)/(4)`
    C
    `(pi)/(3)`
    D
    `(pi)/(2)`

    • Similar Questions

    Explore conceptually related problems

    Two lines with direction cosines l_1,m_1,n_1 and l_2,m_2,n_2 are at righat angles iff (A) l_1l_2+m_1m_2+n_1n_2=0 (B) l_1=l_2,m_1=m_2,n_1=n_2 (C) l_1/l_2=m_1/m_2=n_1/n_2 (D) l_1l_2=m_1m_2=n_1n_2

    The directuion cosines of a line equally inclines to three mutually perpendicular lines hacing D.C.'s as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2),l_(3),m_(3),n_(3) are

    Two lines with direction cosines l_(1),m_(1),n_(1) and l_(2), m_(2), n_(2) are at right angle of

    The angle between the lines whose direction cosines are given by the equatios l^2+m^2-n^2=0, m+n+l=0 is

    The angle between the lines whose direction cosine satisfy the equations l + m + n = 0 and l^(2) =m^(2) +n^(2) is

    Home
    Profile