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Show that the lines : (x+1)/3=(y+3)/5=(z...

Show that the lines : `(x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6)/5` intersect each other. Also find their point of intersection.

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Show that the two lines (x-5)/4=(y-7)/4=(z+3)/-5 and (x-8)/7=(y-4)/1=(z-5)/3 intersect each other . Find also the point of intersection.

Show that the two lines x+1/3=y+3/5=z+5/7 and x-2/1=y-4/3=z-6/5 intersect each other. Find also the point of intersection.

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect each other . Find also the point of intersection.

Show that the lines: (x-1)/3=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)/-2 do not intersect.

Show that the lines (x-1)/23=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)/-2 do not intersect.

The lines x+3y-1=0 and x-4y=0 intersect each other. Find their point of intersection.

Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 intersect. Find the point of intersection and the equaion of the plane contianing them.

Show that the lines : (x-3)/2=(y+1)/-3=(z-2)/4 and (x+2)/2=(y-4)/4=(z+5)/2 are perpendicular to each other.

Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5)/5 are coplanar. Also find the equation of the plane containing the lines.

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

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  2. 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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  3. 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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  4. Prove that the line through A(0,-1,-1) and B(4,5,1) intersects the lin...

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find the angle between the lines whose direction cosines are given by ...

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  18. Find the angle between the lines whose direction cosines are given by ...

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  19. Differentiate the following y=tan(sin(a^x))

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  20. Find the angle of the tirangle ABC whose vertices are A(-1,3,2), B(2,3...

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