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The cartesian equation of a line is 6x -...

The cartesian equation of a line is `6x - 2 = 3y + 1 = 2z - 2`. Find :(a) the direction-ratios of the line, and (b) vector equation of the line parallel to this line and· passing through the point (2, - 1, - 1).

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. A line passes through the point with position vector 2hati-hatj+4hatk...

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  2. Find the vector equation for the line through the points A(3,4,-7) and...

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  3. The cartesian equation of a line is 6x - 2 = 3y + 1 = 2z - 2. Find :(a...

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  4. Find the equations of a line through A(1,-1,0) and parallel to the lin...

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  5. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

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  6. Show that the two lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(...

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  7. Show that the lines : (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6...

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  8. Prove that the line through A(0,-1,-1) and B(4,5,1) intersects the lin...

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  9. Show by direction numbers that the points (-2,4,7),(3,-6,-8) and (1,-2...

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  10. Find the equation of the line passing through the points A(-2,4,7), B(...

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  11. Evaluate int (2x+5)dx/(x^2+4x+5)

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  12. Find the point on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance of 3s...

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  13. Find the angle between the pairs of line with direction ratios lt5,-...

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  14. Find the angle between the pair of lines with directions ratios: <1,1...

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  15. If P,Q are (2,3,-6),(3,-4,5), then find the acute angle that OP makes ...

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  16. Find the angles between each of the following pairs of lines: vecr=4ha...

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  17. Find the angle between the followig pair of lines : (-x+2)/-2=(y-1)/7=...

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  18. Find the angles between each of the following pairs of lines: (x-2)/3=...

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  19. The angle between a line with direction ratios proportional to 2, 2, ...

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  20. Find the angle between the following pair of lines : vecr=hati+hatj-ha...

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