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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 I + `delta`I, m + `delta`m, n + `delta`n, then show that the small angle `delta theta` between the two positions is given by `delta theta^2=deltal^2+deltam^2+deltan^2`.

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The correct Answer is:
`therefore delta theta^2=deltal^2+deltam^2+deltan^2`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
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  2. Find the angle between the lines whose direction cosines are given by ...

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  3. If a variable line in two adjacent positions has direction cosines l, ...

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  4. If O is the origin and A is (a, b, c), then find the direction cosines...

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  5. Two systems of rectangular axis have the same origin. If a plane cuts ...

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  6. Find the foot of perpendicular from the point (2, 3, -8) to the line (...

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  7. Find the distance of a point (2, 4, -1) from the line (x+5)/(1)=(y+3)/...

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  8. Find the length and the foot of perpendicular from the point (1,3/2,2)...

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  9. Find the equation of the line passing through the point (3, 0, 1) and ...

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  10. Find the equation of the plane through the points (2, 1,-1) and (-1, 3...

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  11. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  12. Find the equation of the plane which is perpendicular to the plane 5x ...

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  13. If the plane ax + by = 0 is rotated about its line of intersection wit...

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  14. Find the equation of the plane through the intersection of the planes ...

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  15. Show that the points bari-barj+3bark and 3(bari +barj+bark) are equidi...

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  16. vec(AB)=3bari-barj+bark and vec(CD)= -3bari+2barj+4bark are two vector...

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  17. Show that the straight lines whose direction cosines are given by 2l +...

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  18. If (l1, m1, n1), (l2, m2, n2)" and "(l3, m3, n3) are the direction cos...

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  19. Distance of the point (alpha,beta,gamma) from Y- axis is …........

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  20. If the directions cosines of a line are k, k and k then ..........

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