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Find the value of p so that the lines : ...

Find the value of p so that the lines : `l_1:(1-x)/3=(7y-14)/(2p)=(z-3)/2 and l_2: (7-7x)/(3p)=(y-5)/1=(6-z)/5` are at right angles. also find the equations of the line passing through (3,2,-4) and parallel to line `l_1`.

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Find the value of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2 and (7-7x)/(3p)=(y-5)/1=(6-z)/5 are at right angles.

Find the values of p so that the lines (1-x)/3 = (7y-14)/2p = (z-3)/2 and (7-7x)/3p = (y-5)/1 = (6-z)/5 are at right angles.

Find the equation of the line passing through (1,2,3) and parallel to the planes x-y+2z=5 and 3x+y+z=6.

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.

Show that the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 are coplanar. Also find the equation of the plane containing the lines.

Find the equations of the line through the point (1,2,4) and parallel to the line 3x+2y-z=4, x-2y-2z=5.

Find the cartesian as well as the vector equation of the line passing through : (-1,2,3) and parallel to the line: (x-3)/2=(y+1)/3=(z-1)/6

Find the equations of a line through A(1,-1,0) and parallel to the line (x-2)/3=(2y+1)/2,(5-z)/1 .

Find the equation of plane which passes through the point (1,-1,4) and is parallel to the plane 2x-3y+7z=11 .

Find the cartesian as well as the vector equation of the line passing through : (0,-1,4) and parallel to the straight line : (-x-2)/1=(y+3)/7=(2z-6)/3

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are p...

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

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  3. Find the value of p so that the lines : l1:(1-x)/3=(7y-14)/(2p)=(z-3)/...

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  4. Find k so that the lines : (x-3)/2=(y+1)/3=(z-2)/(2k) and (x+2)/1=(4-y...

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  5. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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  6. Show that the line through the points : (4,7,8), (2,3,4) is parallel t...

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  7. The cartesian equations of a line are 3x + 1 = 6y - 2 = 1 - z. Find th...

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

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  9. Write the equation of a line, parallel to the line (x-2)/-3=(y+3)/2=(z...

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  10. Find the equation of the line perpendicular to the lines : vecr=(3hati...

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  11. Find the equations of the straight line passing through the point (2,...

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  12. Find the equations of the straight line passing through the point (1, ...

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  13. Find the vector and cartesian equations of the line passing through th...

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  14. Find the equation in vector anf cartesian form of the line passing thr...

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  15. Find the equation of the line passing through the point (2, -1, 3) and...

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  16. Prove that the points (1,2,3),(4,0,4),(-2,4,2) and (7,-2,5) are collin...

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  17. Show that the following points whose psitions vectors are given are co...

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  18. Show that the following points whose psitions vectors are given are co...

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  19. Find the points on the line through the points A(1,2,3) and B(5,8, 15)...

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  20. Find the equations of the perpendicular from the point (3,-1,11,) to t...

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