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Find the shortest distance between the f...

Find the shortest distance between the following lines
`vec(r)=hat(i)-hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k))` and ` vec(r)=3hat(i)-hat(j)-2hat(k)+mu(-hat(i)+2hat(j)+hat(k))`

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Verified by Experts

The correct Answer is:
`(5sqrt(2))/(2)`
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Find the shortest distance between the following lines vec(r)=-hat(i)+2hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=hat(i)-hat(j)+2hat(k)+mu(-hat(i)+hat(j)+hat(k)) .

Find the shortest distance between the following lines vec(r)=hat(i)+hat(j)-2hat(k)+lamda(hat(i)+hat(j)+hat(k)) and vec(r)=hat(i)+hat(j)+hat(k)+mu(hat(i)+hat(j)+hat(k))

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Find the shortest distance between the following lines vec(r)=hat(i)+hat(j)+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)+hat(j)-hat(k)+mu(3hat(i)-4hat(j)+hat(k))

Find the shortest distance between the lines vec(r)=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)-hat(j)-hat(k)+mu(3hat(i)-hat(j)+hat(k))

Find the shortest distance between the following lines vec(r)=hat(i)+hat(j)+lamda(hat(i)-hat(k)) and vec(r)=2hat(i)-hat(j)+mu(hat(i)+hat(j)+hat(k))

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Find the shortest distance between the lines vec(r)=hat(i)+2hat(j)+3hat(k)+lamda(2hat(i)+3hat(j)+4hat(k)) and vec(r)=2hat(i)+4hat(j)+5hat(k)+mu(3hat(i)+4hat(j)+4hat(k))

Find the shortest distance between the lines vec(r)=4hat(i)-3hat(j)+lamda(hat(i)+2hat(j)-2hat(k)) and vec(r)=hat(i)+hat(j)-hat(k)-mu(2hat(i)+4hat(j)-4hat(k))

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE
  1. Find the shortest distance between the following lines vec(r)=hat(i)...

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  2. Find the shortest distance between the following lines vec(r)=hat(i)...

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  3. Find the shortest distance between the following lines vec(r)=hat(i)...

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  4. Find the shortest distance between the following lines vec(r)=-hat(i...

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  5. Find the shortest distance between the following lines vec(r)=hat(i)...

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  6. Find the equation of the plane containing the line (x+3)/(2)=(y-2)/(-1...

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  7. Find the equation of the plane through the point (1,1,1) and perpendic...

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  8. Determine whether the lines vec(r)=3hat(i)-hat(j)+lamda(3hat(i)+hat(...

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  9. Find the equation of the plane passing through the points (0,-1,1),(4,...

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  10. Find the equation of the plane passing through the point (1,1,0),(1,2,...

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  11. Find the angle between the following pairs of lines x/2=y/2=z/1 and (x...

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  12. vec(r)=(1-t)hat(i)+(t-2)hat(j)-(3-2t)hat(k) and vec(r)=(1-t)hat(i)(t-...

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  13. Find the angle between these two lines (x+2)/(1)=(y-1)/(-2)=(z-1)/(1) ...

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  14. Find the vector equation of the plane which is at a distance of 7 unit...

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  15. Find the equation of the plane through intersection of the planes : ...

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  16. Find the equation of the plane passing through the points (1,2,-1),(...

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  17. Find the equation of the plane passing through the points (1,1,0),(1...

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  18. Find the direction cosine of a line parallel to the line (2x-5)/(4)=(y...

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  19. Find the equation of the straight line passing through the point (2,-1...

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  20. Find the equation of a plane through the points (1,0,1),(1,2,-2),(2,...

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