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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. Find the angle between the following pairs of lines : (x-2)/2=(y-1)/5=...

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  2. Find the angle between the lines x/2=y/2=z/1 and [x-5]/4=[y-2]/1=[z-3]...

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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. 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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  5. Find the shortest distance between the lines vecr = (hati + 2hatj+hatk...

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  6. Find the shortest distance between the lines ((x+1)/7=(y+1)/-6=(z+1)/1...

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  7. Find the shortest distance between the lines whose vector equations ar...

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  8. Find the shortest distance between the following lines whose vector eq...

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  9. In the following case, determine the direction cosines of the normal ...

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  10. In the following case, determine the direction cosines of the normal ...

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  11. In each of the following cases, determine the direction cosines of the...

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  12. In the following case, determine the direction cosines of the normal ...

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  13. Find the vector equation of a plane, which is at a distance of 7 units...

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  14. Find the cartesian equations of the following planes: vecr*(4hati+8hat...

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  15. Find the cartesian equations of the following planes: vecr*(2hati+3hat...

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  16. Find the cartesian equations of the following planes:⃗ r ⋅ [ ( s − 2 t...

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  17. In the following case, find the coordinates of the foot of the perpend...

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  18. In the following case, find the coordinates of the foot of the perpend...

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  19. In the following cases, find the co-ordinates of the foot of the perpe...

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  20. In the following case, find the coordinates of the foot of the perpend...

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