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If O is the origin and A is (a, b, c), t...

If O is the origin and A is (a, b, c), then find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

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The correct Answer is:
`therefore ax+by+cz=a^2+b^2+c^2`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
  1. Find the angle between the lines whose direction cosines are given by ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The distance of the plane barr.(2/7i+3/7j-6/7k)=1 from the origin is …...

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