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Show that the lines (x-1)/(4)=(2-y)/(6...

Show that the lines ` (x-1)/(4)=(2-y)/(6)=(z-4)/(12) ` and ` (x-3)/(-2)=(y-3)/(-2)=(5-z)/(6) ` are parallel.

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The correct Answer is:
` -2hati+3hatj-6hatk `
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Show that the lines (x-1)/4=(2-y)/(6)=(z-4)/(12) and (x-3)/(-2)=(y-3)/(3)=(5-z)/(6) are parallel.

Show that the lines (x-3)/(2)=(y-5)/(-1)=(z+7)/(4) and (x-15)/(4)=(y+12)/(-2)=(z-8)/(8) are parallel.

Show that the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(3)and(x-1)/(-3)=(y-4)/(2)=(z-5)/(1) are coplanar. Also, find the plane containing these lines.

Show that the lines (x-1)/(3)=(y+1)/(2)=(z-1)/(5)and(x+2)/(4)=(y-1)/(3)=(z+1)/(-2) do not intersect.

Show that the lines (x-3)/(1)=(y-5)/(-2)=(z-7)/(1) and (x-1)/(7)=(y-1)/(6)=(z-1)/(7) are skew lines and find the shortest distance between them.

The line through of the plane passing through the lines (x-4)/(1)=(y-3)/(1)=(z-2)/(2) and (x-3)/(1)=(y-2)/(-4)=(z)/(5) is

The straight lines (x-3)/(2)=(y+5)/(4)=(z-1)/(-13)and(x+1)/(3)=(y-4)/(5)=(z+2)/(2) are

Find tha angle between the lines (x-20)/(1)=(y+15)/(2)=(z-3)/(-2) and (x+5)/(6)=(y+3)/(3)=(z-16)/(6)

Find the shortest distance berween the following pairs of lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1)and(x-3)/(-3)=(y+7)/(2)=(z-6)/(4)

Find the point of intersection of the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z .

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Show that the lines (x-1)/(4)=(2-y)/(6)=(z-4)/(12) and (x-3)/(-2...

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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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