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Find the distance of the point (-1 , -5 ...

Find the distance of the point (-1 , -5 , -10) from the point of intersection of the line `vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk)` and the plane `vecr.(hati-hatj+hatk)`=5.

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The correct Answer is:
`=sqrt169 =13` units
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Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

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ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 6 MARKS:
  1. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  2. Find the direction cosines of a line which makes equal angles with the...

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  3. If the equations of a line AB are (3-x)/1 = (y+2)/-2 = (z-5)/4, then t...

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  4. If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4, w...

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  5. Find the vector equation of a line passing through (2, -1, 1) and para...

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  6. Find the vector equation of the line through the point (2,-1,-1) and i...

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

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  8. Find the coordinates of the point where the line through (3, 4, 1) and...

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  9. Find the coordinates of the point where the line through (3, – 4, – 5)...

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

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  11. Find the vector and cartesian equation of a line through the point (1,...

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  12. Find the vector and cartesian equation of the line passing through the...

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

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  14. Find the equation of a line passing through the points A(0, 6, -9) and...

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  15. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

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  16. Find the co ordinates of the foot of perpendicular and the length of t...

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  17. Find the shortest distance between the lines : vecr=hati-hatj+lamda(...

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

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  19. Find the shortest distance between the lines vecr=hati+2hatj+3hatk+lam...

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  20. Find the shortest distance (S.D.) between the lines : vecr=hatj+lamd...

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  21. Write the vector equation of the following lines and hence find distan...

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