Home
Class 12
MATHS
If the direction cosines of two lines ar...


If the direction cosines of two lines are `(l_(1), m_(1), n_(1))` and
`(l_(2), m_(2), n_(2))` and the angle between them is `theta` then
`l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2)`
and costheta` = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2)`
If `l_(1)=1/sqrt(3), m_(1)=1/sqrt(3)` then the value of `n_(1)` is equal to

A

`pm 1/sqrt(3)`

B

`+ 1/sqrt(3)`

C

` -1/sqrt(3)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - D COMPREHENSION II|3 Videos
  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - D COMPREHENSION III|3 Videos
  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - C|14 Videos
  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos
  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) The angle between the lines whose direction cosines are (1/2, 1/2,1/sqrt(2)) and (-1/2, -1/2, 1/sqrt(2)) is

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

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines.

If the direction cosines of a straight line are l,m and n, then prove that l^(2)+m^(2)+n^(2)=1

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

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

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).

The direction cosines of the lines bisecting the angle between the lines whose direction cosines are I_(1),m_(1),n_(1) and I_(2),m_(2),n_(2) and the angle between these lines is theta ,are