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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.

FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. Find the angle between the following lines (x-1)/(2)=(y+1)/(3)=(z-4)...

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

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

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  4. Show that the lines (x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and (x-4)/(2)=...

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  5. find the shortest distance between the skew lines. vecr=(veci-vecj)+...

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  6. find the shortest distance between the skew lines. vecr=(2veci-vecj-...

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  7. Find the vector and cartesian equations of a plane which is at a dista...

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  8. The unit normal vector to the plane 2x - y + 2z = 5 are …………..

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  9. Find the length of the perpendicular from the origin to the plane ve...

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  10. The foot of the perpendicular drawn from the origin to a plane is 18 ,...

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  11. Find the Cartesian equation of the plane through the point with positi...

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  12. Find the vector and cartesian equations of the plane passing through t...

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

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  14. Find the vector and cartesian equation of the plane passing through th...

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  15. Find the vector and cartesian equations of the plane passing through t...

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  16. Find the vector and cartesian equations of the plane passing through t...

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

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  18. Find the vector and cartesian equations of the plane containing the li...

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  19. Derive the equation of the plane in the intercept form.

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  20. Find the Cartesian form of the equation of the plane vec(r)=(s-2t)hat(...

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