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Find the angle between the following pai...

Find the angle between the following pair of lines : `vecr=hati+hatj-hatk+lambda(hati-3hatj+2hatk), vecr=2hati-hatj+hatk+mu(3hati+hatj-2hatk)`

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Find the angle between the following pair of lines: vecr = 3hati+hatj-2hatk + lambda(hati-hatj-2hatk) and vecr = 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the angle between the following pairs of lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) , vecr=5hatj-2hatk+mu(3hati+2hatj+6hatk)

Find the angles between each of the following pairs of lines: vecr=4hati-hatj+lambda(hati+2hatj-hatk) and vecr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

Find the angle between the following pair of lines: vecr = 2hati-5hatj+hatk + lambda(3hati+2hatj+6hatk) and vecr = 7hati-6hatj+mu(hati+2hatj+2hatk)

Find the shortest distance between each of the following pair of lines: vecr=3hati+5hatj+7hatk+lambda(hati-2hatj+7hatk) and vecr=-hati-hatj-hatk+mu(7hati-6hatj+hatk) .

Find the angle between the pair of lines given by vecr = 3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr = 5hati-2hatj+mu(3hati+2hatj+6hatk)

Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

Find the shortest distance and the equation of the shortest distance between the following two lines: vecr=(-hati+hatj+9hatk)+lambda(2hati+hatj-3hatk) and vecr=(3hati-15hatj+9hatk)+mu(2hati-7hatj+5hatk)

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

Find the angle between the pair of lines vecr=2hati-5hatj+hatk+lamda(3hati+2hatj+6hatk) and vecr=7hati-6hatk+mu(hati+2hatj+2hatk)

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the angle between the following pair of lines : vecr=hati+hatj-ha...

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  2. Find the distance of the point (2,3,4) from the x axis.

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  3. If a line makes angles of 90^@,60^@ and theta with the x, y and z axis...

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  4. If a line has direction cosines <2/3, -1/3, -2/3>, then find the direc...

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  5. If a line has direction ratios <2,-1,-2>, then what are its direction ...

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  6. Find the direction cosines of a line passing through the points (1,0,0...

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  7. Find the direction cosines of the lines joining the points: (-1,-1,-1)...

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  8. Find the direction ratios and direction cosines of the vector joining ...

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  9. Write the direction cosines of the vector : -2hati+hatj-5hatk

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  10. Write the direction cosines of the vector : hati+2hatj+3hatk

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  11. Find the length of the projection of the line segment joining (3,4,5) ...

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  12. Show that the following points are collinear : (1,2,3) , (2,6,3) , (3,...

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  13. Find the acute angle between two lines whose direction ratios are <2,3...

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  14. Find the obtuse angle between two lines whose direction ratios are : <...

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  15. Find the angle between the lines whose direction ratios are : a,b,c...

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  16. Find the direction cosines of the sides of the triangle whose vertices...

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  17. Show that the three lines with direction cosines 12/13, -3/13, -4/13, ...

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  18. The angle between the lines whose direction cosines are given by the ...

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  19. Find the angle between the lines whose direction cosines are given by ...

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  20. Find the area of the triangle ABC whose vertices are : A(1,2,4), B(-2,...

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  21. Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel...

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