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Find the shortest distance between the lines `L_(1) " and " L_(2)` given by
`vec( r )=hat(i) +hat(j) +lambda(2hat(i)-hat(j)+hat(k)) " and " vec(r )=2hat(i) +hat(j)-hat(k) +mu (4hat(i) -2hat(j) +2hat(k))`

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The correct Answer is:
`= (10)/(sqrt(59))`
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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 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 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 distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )

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)) .

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 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 magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

OSWAAL PUBLICATION-THREE DIMENSIONAL GEOMETRY-Topic -2 (Short answer type questions-II)
  1. Find the equation of the line which passes through the point (1,2,3) a...

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

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  3. Find the shortest distance between the lines L(1) " and " L(2) ...

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  4. Find the coordinates of the foot of perpendicular drawn from th poi...

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  5. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  6. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Als...

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  7. Find the shortest distance between two lines whose vector equations ar...

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  8. Show that the lines (x+1)/(3)=(y+3)/(5) =(z+5)/(7) " and " (x-2)/(1...

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  9. Show that the lines (5-x)/-4=(y-7)/4=(z+3)/-5 and (x-8)/7=(2y-8)/2=(z-...

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  10. Show that the lines vec(r)= vec(i)+vec(j)-vec(k)+lambda(3 vec(i)- vec(...

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  11. The equation of line passing through (3,-1,2) and perpendicular to the...

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  12. Find the equation of the line passing through the point (2, 1, 3) and ...

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  13. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

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  14. Find the shortest distance between the lines whose vector equations ar...

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  15. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

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  16. Using vectors show that the points A(-2,3,5),B(7,0,-1)C(-3,-2,-5) and ...

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  17. Show that the lines vec(r ) =(hat(i) -hat(j)) +lambda (2hat(i)+ ha...

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  18. Find the Vector and Cartesian equations of the line passing through...

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  19. Find the shortest distance between the following pair of lines : (...

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  20. 2/ Find the perpendicular distance of the point (1, 0, 0) from the lin...

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