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Show that the lines vecr=(hati-hatj)+t(2...

Show that the lines `vecr=(hati-hatj)+t(2hati+hatk)` and `vecr=(2hati-hatj)+s(hati+hatj-hatk)` are skew lines and find the distance between them .

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The correct Answer is:
`(1)/(sqrt(14))`
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Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Show that the lines vecr=(3hati+5hatj+7hatk)+t(hati-2hatj+hatk) vecr=(hati+hatj+hatk)+s(7hati+6hatj+7hatk) are skew lines and find the shortest distance between them.

Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hatj-3hatk)+s(hati+2hatj+3hatk) are parallel. Find the shortest distance between them.

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

Show that the lines vecr=(-2hati-4hatj-6hatk)+t(hati+4hatj+7hatk) vecr=(hati+3hatj+5hatk)+s(3hati+5hatj+7hatk) are coplanar. Find the equation of such plane in non parametric form and in cartesian form.

Given the straight lines vecr=(3hati+2hatj-4hatk)+lambda(hati+2hatj+2hatk) and vecr=(5hatj-2hatk)+mu(3hati+2hatj+6hatk) i.Find the angle between the lines. ii. Obtain a unit vector perpendicular to both the lines. iii. Form the equation of the line perpendicular to the given lines and passing through the point (1,1,1).

Find the acute angle between the planes vecr(2hati-3hatj+5hatk)=1 and vecr(hati-hatj-hatk)=7 .

Statement 1 : Lines vecr= hati-hatj+ lamda (hati+hatj-hatk) and vecr= 2hati-hatj+ mu (hati+hatj-hatk) do not intersect. Statement 2 : Skew lines never intersect.

PREMIERS PUBLISHERS-APPLICATIONS OF VECTOR ALGEBRA-PROBLEMS FOR PRACTICE (Answer the following questions)
  1. Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vec...

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  2. Find the vector and cartesian equation of the line through the point (...

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  3. Find the vector and cartesian equation of the line joining the points ...

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  4. Find the angle between the lines (x-1)/(2)=(y+1)/(3)=(z-4)/(6) and vec...

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  5. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

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  6. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

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  7. Find the vector and cartesian equation of a plane which is at a distan...

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  8. Find the vector and cartesian equation of the plane passing through (2...

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  9. Find the vector and cartesian equation of the plane passing through (2...

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  10. Find the Vector and Cartesian equation of the plane containing the lin...

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  11. Find the vector cartesian equation of the plane passing through the po...

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  12. Find the vector and certesian equation of the plane through the points...

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  13. Find the equation of the plane passing through the points (3, 4, 2), (...

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  14. Find the equation of the plane passingthrough the intersection of the...

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  15. Find the distance between the parallel planes vecr*(-hati-hatj+hatk)=3...

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  16. Find the coordinates of the point where the line vecr=(hati+2hatj-5ha...

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  17. The value of [hati+hatj,hatj+hatk,hatk+hati] is equal to :

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  18. If abs(veca+vecb)=abs(veca-vecb) prove that veca and vecb are perpendi...

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  19. Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3...

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  20. Show that the lines vecr=(4veci+5vecj+6veck)+t(2veci+3vecj+4veck) and ...

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