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Determine whether the pair of straight l...

Determine whether the pair of straight lines
`vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hatj-3hatk)+s(hati+2hatj+3hatk)` are parallel. Find the shortest distance between them.

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Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hati-3hatk)+s(hati+2hatj+3hatk) are parallel.

Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

Show that the lines vecr=(3hati+5hatj+7hatk)+t(hati-2hatj+hatk) vecr=(hati+hatj+hatk)+s(7hati+6hatj+7hatk) are skew lines and find the shortest distance between them.

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hatj)+s(hati+hatj-hatk) are skew lines and find the distance between them .

Find the angle between the following lines. vecr=(4hati-hatj)+t(hati+2hatj-2hatk) vecr =(hati-2hatj+4hatk)+s(-hati-2hatj+2hatk)

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk...

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  2. The work done by the force vecF=ahati+hatj+hatk in moving the point...

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  3. If the position vectors of three points A, B and Care respectively v...

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  4. A force given by and 3veci+2vecj-4veck is applied at the point (1,-1...

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  5. Show that the area of a parallelogram having diagonals 3veci+vecj-2v...

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  6. If the edges  veca=-3veci+7vecj+5veck , vecb=-5veci+7vecj-3veck ,...

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  7. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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  8. The volume of the parallelepiped whose edges are represented by -12 ha...

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  9. Prove that |vecavecbvecc|=abc   if and only if veca , vecb , ...

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  10. Show that the points (1, 3, 1), (1, 1,-1), (-1, 1, 1), (2,2, -1) are l...

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  11. If veca=2veci+3vecj-5veck , vecb=-veci-vecj+2veck and vecc=4vec...

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  12. If veca =3veci+2vecj-4veck , vecb =5veci-3vecj+6veck , vecc =5ve...

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  13. If veca =2veci+3vecj-veck , vecb =2veci+5veck , vecc =vecj-3veck...

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  14. Find the vector and cartesian equations of the straight line passing t...

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  15. Find the vector and cartesian equations of the straight line passing t...

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  16. Find the angle between the following lines vecr=3veci+2vecj-veck+t(v...

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  17. Find the angle between the following lines (x-1)/(2)=(y+1)/(3)=(z-4)...

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  18. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

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  19. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

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  20. Show that the lines (x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and (x-4)/(2)=...

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  21. find the shortest distance between the skew lines. vecr=(veci-vecj)+...

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