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Prove that the straight lines whose dire...

Prove that the straight lines whose direction cosines are given by the relations `al+bm+cn=0 and fmn+gnl+hlm=0` are
Perpendicular to each other if `(f)/(a)+(g)/(b)+(h)/(c)=0`, and
parallel if `a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2bcgh-2cahf-2abfg=0`.

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MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -REVISION EXERCISE
  1. If the direction cosines of a variable line in two adjacent points be ...

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  2. Prove that the straight lines whose direction cosines are given by the...

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  3. Prove that the line joining the mid-points of the two sides of a tr...

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  4. Find the vector equation of the line passing through (1, 2, 3) and ...

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  5. Prove that the lines x=ay +b,z =cy +d and x=a'y +b' z =c'y +a' ...

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  6. Prove that the line joining the points vec(6a) - vec(4b) + vec(4c) and...

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  7. Find the vector equation o the line passing through (1,2,3) and parall...

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  8. Find the vector equation of the line passing through the point (1,"...

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  9. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  10. Show that equation of the plane passing through a point having positio...

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  11. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  12. Find the distance of the point with position vector - hati - 5 hatj - ...

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  13. Find the point R, Where the line joining P (1,3,4) and Q (-3,5,2) cuts...

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  14. Find the equation of the plane passing through the line of intersectio...

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  15. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  16. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  17. Find the equation of the plane , which contains the line of intersecti...

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  18. Prove that the shortest distance between the diagonals of a rectangula...

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  19. A variable plane is at a constant distance p from the origin and meets...

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