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Find the angles between each of the foll...

Find the angles between each of the following pairs of lines:
`vecr=4hati-hatj+lambda(hati+2hatj-hatk)` and `vecr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)`

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Find the shortest distance between each of the following pair of lines: vecr=(4hati-5hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

Find the angle between the following pair of lines: vecr = 3hati+hatj-2hatk + lambda(hati-hatj-2hatk) and vecr = 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the shortest distance between each of the following pair of lines: vecr=3hati+5hatj+7hatk+lambda(hati-2hatj+7hatk) and vecr=-hati-hatj-hatk+mu(7hati-6hatj+hatk) .

Find the angle between the following pair of lines: vecr = 2hati-5hatj+hatk + lambda(3hati+2hatj+6hatk) and vecr = 7hati-6hatj+mu(hati+2hatj+2hatk)

Find the angle between the following pair of lines : vecr=hati+hatj-hatk+lambda(hati-3hatj+2hatk), vecr=2hati-hatj+hatk+mu(3hati+hatj-2hatk)

Find the angle between the following pairs of lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) , vecr=5hatj-2hatk+mu(3hati+2hatj+6hatk)

Find the angle between the pair of lines vecr=2hati-5hatj+hatk+lamda(3hati+2hatj+6hatk) and vecr=7hati-6hatk+mu(hati+2hatj+2hatk)

Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

Find the shortest distance between the following lines whose vector equations are : vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk)

Determine whether or not the following paris of lines intersect: vecr=hati-hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati-hatj-hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the angle between the pair of lines with directions ratios: <1,1...

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

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

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

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

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

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

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

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

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

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

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  12. Find the length of the perpendicular from the point (1,2,3) to the lin...

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  13. Find the perpendicular distance of the point (1,0,0) from the line : (...

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  14. Find the equations of the perpendicular drawn from the point (2,4,-1) ...

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  15. Find the length and foot of perpendicular drawn from the point (2,-1,3...

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

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

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  18. Show that, if the axes are rectangular, the equations of the line thro...

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  19. Find the coordinates of the foot of the perpendicular drawn from point...

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  20. A(1,0,4), B(0,-11,3), C(2,-3,1) are three points and D is the foot of ...

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