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Find the angle between the lines vec...

Find the angle between the lines
`vecr = (3 + lambda)hati + 2(1 + lambda)hatj + 2(1 – 2lambda)hatk` and `vecr=5hatj-2hatk+mu(3hati+2hatj-6hatk).`

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The correct Answer is:
Angle `theta=cos^(-1)((19)/(21))`
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Find the shortest distance between the lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

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Find the shortest distance between the lines vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

Find the shortest distance between the lines whose vector equations are vecr=(hati+2hatj+3hatk)+lambda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

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-TEXTBOOK IILUSTRATIONS FOR PARCTICE WORK
  1. Find the vector equation for the line passing through the points (-1, ...

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  2. The Cartesian equation of a line is (x+3)/(2)=(y-5)/(4)=(z+6)/(2) ...

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  3. Find the angle between the lines vecr = (3 + lambda)hati + 2(1 + l...

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  4. The angle "bet"^(n) two line ( x+3)/(3) = (y-1)/(5) = (z +3)/(4...

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  5. Find the shortest distance between the lines l1 and l2 whose vector eq...

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  6. Find the distance between the lines l1 and l2 given by vecr=hati+2hatj...

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  7. Find the vector equation of the plane which is at a distance of (6)/(s...

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  8. Find the direction cosines of the unit vector perpendicular to the pla...

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  9. Find the distance of the plane 2x – 3y + 4z - 6 = 0 from the origin.

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  10. Find the coordinates of the foot of the perpendicular drawn from the o...

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  11. Find the vector and cartesian equations of the plane which passes thro...

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  12. Find the vector equations of the plane passing through the points R(2,...

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  13. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y ...

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  14. Find the vector equation of the plane passing through the intersection...

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

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  16. Find the angle between the two planes 2x + y - 2z = 5 and 3x – 6y – 2z...

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  17. Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2...

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  18. Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3ha...

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

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  20. A line makes the angle alpha, beta , gamma and delta with the diagonal...

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