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Show that the line joining the origin to...

Show that the line joining the origin to the point `(2,1,1)` is perpendicular to the line determined by the points `(3,5,-1)` and `(4,3,-1)dot`

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Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -10 and (4, 3, -1).

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Show that the line joining the points (4,-3) and (0,7) is perpendicular to the line joining the points (5,2) and (0,0) .

Show that the line joining the points (2,-6) and (-4,-8) is perpendicular to the line joining the points (4,-2) and (6,-8) .

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Show that the line joining the points (1,2,3), (-1,-2,-3) is perpendicular to the line joining (-2,1,5),(3,3,2).

Show that the line through the points (1, 1, 2), (3, 4, 2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Determine the value of k so that the line joining points A(k,1,-1) and B(2,0,2k) is perpendicular to the line joining the points C(4,2k,1) and D(2,3,2) .

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RD SHARMA ENGLISH-DIRECTION COSINES AND DIRECTION RATIOS-All Questions
  1. Show that the points (2,3,4),(-1,-2,1),(5,8,7) are collinear.

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  2. Find the acute angle between the lines whose direction ratios are p...

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  3. Show that the line joining the origin to the point (2,1,1) is perpe...

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  4. Find the angle between the lines whose direction ratios are proport...

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  5. Find the angle between the vectors whose direction cosines are prop...

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  6. Find the angle between the vectors with direction ratios proportion...

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  7. Show that the line through points (4,7,8) and 2,3,4) is parallel to...

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  8. If the coordinates of the points A ,B ,C ,D are (1,2,3),(4,5,7),(-4,3...

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  9. Find the direction cosines of the lines, connected by the relations...

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  10. Find the direction cosines of the two lines which are connected by t...

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  11. A line makes angles alpha,""""beta,""""gamma and delta with the ...

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  12. Show that the straight lines whose direction cosines are given by th...

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  13. If a variable line in two adjacent positions has direction cosins l ...

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  14. If the edges of a rectangular parallelepiped are a ,b ,c prove that th...

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  15. If three mutually perpendicular lines have direction cosines (l1,m1,n...

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  16. Find the direction cosines of the sides of the triangle whose verti...

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

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  18. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  19. Given that P(3,2,-4),Q(5,4,-6)a n dR(9,8,-10) are collinear. Find the ...

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  20. Find the coordinates of the foot of the perpendicular drawn from th...

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