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The equation of a line which passes through the point ` ( 1, 2 , 3 ) ` and is parallel to the vector ` 3 hati + 2 hatj - 2 hatk ` , is

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The cartesian equation of a line passing through the point (3,2,1) and is parallel to the vector 2hati + 2hatj - 3hatk is

The equation of a line passing through the point (4,-2,5) and parallel to the vector 3hati -hatj + 2hatk is

Find the vector equation of a line through the point (-3, 2, -4) and is parallel to the vector 3hati + 2hatj+ 4hatk .

The distance of the point having position vector -hati+ 2 hatj + 6 hatk from the straight line passing through the point (2,3,-4) and parallel to the vector, 6 hati+ 3 hatj -4 hatk is :

The distance of the point P(1,2,3) from the line which passes through the point (4,2,2) and parallel to the vector 2hati+3hatj+6hatk is

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is

Find the equation of a line passing through the point (2,-3,5) and parallel to vector (3hati+2hatj-hatk) .

Find the vector and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -NCERT-FILE (EXERCISE 11.2)
  1. Show that the three lines with direction cosines (12)/(13),(-3)/(13),...

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  2. Show that the line through the points (1,-1,2) and (3,4-2) is perpe...

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

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  4. The equation of a line which passes through the point ( 1, 2...

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  5. Find the equation of the line in vector and in cartesian form that ...

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  6. Find the cartesian equation of the line which passes through the poin...

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  7. The vector equationm of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is

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  8. Find the vector and Cartesiasn equation of the line that passes throug...

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  9. Find the vector and the cartesian equations of the line that passes th...

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  10. Find the angle between the following pairs of lines : (i)vec(r) = 2 ...

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  11. Find the angle between the following pair of lines , (i) (x - 2)/(2)...

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  12. Find the values p so that line (1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(7-7x)...

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  13. Show that the lines (x+5)/(7) = (y +2)/(-5) = (z)/(1) and (x)/(1) = (y...

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  14. Find the shortest distance betwee the lines : vec(r) = (hati + 2 hat...

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  15. Find the shortest distance between the lines ( x + 1 ...

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

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  17. Find the shortest distance between the following lines whose vector...

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