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If a variable line in two adjacent posit...

If a variable line in two adjacent positions has direction cosines (l,m,n) and `(l + delta l, m + delta m, n + delta n)` , then show that the small angle `delta theta` between the two position is given by `(delta theta)^(2) = (delta l)^(2) + (delta m)^(2)+ (delta n)^(2)`

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The correct Answer is:
`(delta theta)^(2)`
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AAKASH SERIES-DIRECTION COSINES & RATIOS-PRACTICE EXERCISE
  1. If a variable line in two adjacent positions has direction cosines (l,...

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  2. Match the following {:("List-1","List-II"),("(A)D.C's of x-axis",(1)...

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  3. The number of lines which are equally inclined to the coordinate axe...

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  4. If the d.c.s of the line joining the oints P(4,3,5) and Q(1,1,k) are (...

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  5. If d.c's of the line joining the origin and a point unit distance from...

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  6. If (1,2,-2) are the D.R's of a line then Statement-I : The D.C's of t...

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  7. Assertion (A) : If a line make angles 45^(@), 45^(@) with the x and y ...

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  8. If a line makes angles cos^(-1)(1//5),cos^(-1)(3//5) with X and Y- axe...

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  9. The angle between the two lines whose direction cosines are ((sqrt(3))...

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  10. The angle between the line passing through the points (3,1,-2) and (4...

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  11. If the d.r's of two lines are (x,3,5) and (2,-1,2) and if the anlgle ...

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  12. The d.r.s of two perpendicular lines are 1,-3,5 and lambda,1 + lambda...

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  13. If the line joining the points (-1,2,3) (2,-1,4) is perpendicular to t...

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  14. If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then direc...

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  15. If the line joining the points (1,4,2) and (-2,1,2) is inclined at an...

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  16. If the d.r's of bar(OA),bar(OB) are (1,-2,3),(-3,4,5) then the d.c's ...

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  17. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are d.c's of two lines then find ...

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  18. If the d.c's of the two lines are (2)/(3),(2)/(3),(1)/(3),(5)/(13),(12...

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  19. If (6,-2,-3),(1,2,2) are d.r's of two lines then the d.c's of line bis...

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  20. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are direction cosines of two line...

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  21. If the d.c's (l,m,n) of two lines are related as l + m + n = 0, 2lm -...

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