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Find the shortest distance between the l...

Find the shortest distance between the lines.
`r=(hat(i)+2hat(j)+hat(k))+lambda(hat(i)-hat(j)+hat(k)) " and " r=(2hat(i)-hat(j)-hat(k))+mu(2hat(i)+hat(j)+2hat(k))`.

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The correct Answer is:
`(3sqrt(2))/2` units
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Find the angle between the following pairs of lines : r=3hat(i)+hat(j)-2hat(k)+lambda(hat(i)-hat(j)-2hat(k)) " and " r=2hat(i)-hat(j)-56hat(k)+mu(3hat(i)-5hat(j)-4hat(k)) .

Find the angle between the following pairs of lines : r=2hat(i)-5hat(j)+hat(k)+lambda(3hat(i)+2hat(j)+6hat(k)) " and " r=7hat(i)-6hat(k)+mu(hat(i)+2hat(j)+2hat(k))

Find the distance between the parallel lines vec(r)=hat(i)+2hat(j)-4hat(k)+m(2hat(i)+3hat(j)+6hat(k)) " and " vec(r)=3hat(i)+3hat(j)-5hat(k)+n(2hat(i)+3hat(j)+6hat(k))

Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))

Find the angle between the pair of lines vec(r)=3hat(i)+5hat(j)-hat(k)+lambda(hat(i)+hat(j)+hat(k))" and "vec(r)=7hat(i)+4hat(k)+mu(2hat(i)+2hat(j)+2hat(k))

Find the sum of vectos a = hat(i)- 2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k) and c=hat(i)-6hat(j)-7hat(k) .

Find the shortest distance between two lines whose vector equations are vec(r) = (hat(i) + 2 hat(j) + 3 hat(k))+lambda(hat(i)- 3hat(j) + 2 hat(k)) and vec(r) = (4 hat(i) + 5 hat(j) + 6 hat(k))+ mu (2 hat(i)+3 hat(j) + hat(k)) .

Find the shortest distance between the lines whose vector equations are vec(r) = (hat(i) + hat(j)) + lambda(2 hat(i) - hat(j) + hat(k)) and vec(r) = (2 hat(i) + hat(j) - hat(k)) + mu (3 hat(i) - 5 hat(j)+2 hat(k)) .

Find the angle between the following pairs of lines : vec(r)=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) " & " vec(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) Note : Angle between two lines is the angle between vec(b_(1)) " and " vec(b_(2))

SUBHASH PUBLICATION-THREE DIMENSIONAL GEOMETRY-THREE MARKS QUESTIONS WITH ANSWERS
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  2. Find the shortest distance between the lines. (x+1)/7=(y+1)/(-6)=(z+...

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  3. Find the angle between the following pairs of lines : vec(r)=3hat(i)...

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  4. Find the angle between the following pairs of lines : r=2hat(i)-5hat...

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  5. Find the angle between the following pairs of lines : r=3hat(i)+hat(...

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  6. Find the angle between the following pairs of lines : (x-2)/2=(y-1)...

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  7. Find the angle between the following pairs of lines : x/2=y/2=z/1 " ...

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  8. Find the distance between the parallel lines vec(r)=hat(i)+2hat(j)-4ha...

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  9. Find the angle between the planes whose vector equations are vec(r)*...

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  10. Find the angle between the planes whose vector equations are 3x-6y+2...

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  11. Find the angle between the line (x+1)/2=y/3=(z-3)/6 and the plane 10x+...

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  12. In the following cases, find the coordinates of the foot of the perpen...

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  13. In the following cases, find the coordinates of the foot of the perpen...

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  14. In the following cases, find the coordinates of the foot of the perpen...

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  15. In the following cases, find the coordinates of the foot of the perpen...

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  16. Find the vector and Cartesian equations of the planes. That passes t...

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  17. Find the vector and Cartesian equations of the planes. That passes t...

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  18. Find the equation of the planes that passes through the sets of three ...

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  19. Find the equation of the planes that passes through the sets of three ...

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