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Find the shortest distance between the lines `vecr =(8+3lambda) hati - (9 +16lambda) hatj+(10+7lambda)hatk` and `vecr= (15hati + 29hatj + 5hatk) + mu(3hati + 8hatj - 5hatk ).`

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The correct Answer is:
`=14 units`
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Find the shortest distance between the lines l_1 and l_2 whose vector equations are vecr=hati+hatj+lambda(2hati-hatj+hatk) and vecr=2hati+hatj-hatk+mu(3hati-5hatj+2hatk).

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
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  2. Find the equation of the plane through the points (2, 1,-1) and (-1, 3...

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  3. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  4. Find the equation of the plane which is perpendicular to the plane 5x ...

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  6. Find the equation of the plane through the intersection of the planes ...

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  7. Show that the points bari-barj+3bark and 3(bari +barj+bark) are equidi...

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  8. vec(AB)=3bari-barj+bark and vec(CD)= -3bari+2barj+4bark are two vector...

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  9. Show that the straight lines whose direction cosines are given by 2l +...

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  10. If (l1, m1, n1), (l2, m2, n2)" and "(l3, m3, n3) are the direction cos...

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  11. Distance of the point (alpha,beta,gamma) from Y- axis is …........

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  12. If the directions cosines of a line are k, k and k then ..........

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  13. The distance of the plane barr.(2/7i+3/7j-6/7k)=1 from the origin is …...

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  14. The sine of the angle between the straight line (x-2)/(3)=(y-3)/(4)=(z...

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  15. The reflection of the point (alpha,beta,gamma) in the xy - plane is .....

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  16. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4...

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  17. The locus represented by xy + yz = 0 is .........

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  18. The plane 2x – 3y + 6z - 11 = 0 makes an angle sin^(-1)alpha with X- a...

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  19. A plane passes through the points (2, 0, 0) (0,3,0) and (0, 0, 4). The...

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  20. The direction cosines of the vector 2bari + 2barj - bark are ............

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