Home
Class 11
MATHS
If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are...

If `(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))` are d.c's of two lines then find the value of `(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)`

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND RATIOS

    AAKASH SERIES|Exercise EXERCISE - 7.1 (VERY SHORT ANSWER QUESTION)|23 Videos

  • DIRECTION COSINES AND RATIOS

    AAKASH SERIES|Exercise EXERCISE - 7.1 (SHORT ANSWER QUESTION)|11 Videos

  • DIRECTION COSINES AND RATIOS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|8 Videos

  • DIRECTION COSINES & RATIOS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|36 Videos

  • DOT PRODUCT OF TWO VECTORS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|57 Videos

Similar Questions

Explore conceptually related problems

If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are d.c's of two lines whose angle between them is 30^(@) , then d.c's of a line perpendicular to both these lines are k(m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1)) , k =

Show that the condition that tha concurrent lines with direction cosines (l_(1).m_(1),n_(1)),(l_(2),m_(2),n_(2))and(l_(3),m_(3),n_(3)) are coplanar is l_(1)(m_(2)n_(3)-m_(3)n_(2))+m_(1)(n_(2)l_(3)-n_(3)l_(2))+n_(1)(l_(2)m_(3)-l_(3)n_(2))=0

If (l_(1),m_(1),n_1),(l_(2),m_(2),n_(2)) are d.c.s of two intersecting lines, show that d.c.s of two lines bisecting the angles between them are proportional to l_(1)+l_(2),m_(1)+m_(2),n_(1)+n_(2).

If l^(2)+m^(2)=1 then the max value of l+m is

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two vectors and theta is the angle between them, then the value of cos theta is

If (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) are the direction cosines of two lines find the direction cosines of the line which is perpendicular to both these lines.