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Find the vector equation of the followin...

Find the vector equation of the following plane in scalar product form: `vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`

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Find the vector equation of the following planes in scalar product form: vecr=2hati-hatk+lambdahati+mu(hati-2hatj-hatk) .

Find the vector equation in scalar product form of the plane vecr=2hati-hatj+lambda(hati+2hatj+3hatk)+mu(2hati-hatj-3hatk) .

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 equation of the plane containingg the lines: vecr=hati+hatj+lambda(hati+2hatj-hatk) and vecr=hati+hatj+mu(-hati+hatj-2hatk) . Find the distance of this plane from origin and also from the point (1,1,1).

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

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)

Determine whether or not the following paris of lines intersect: vecr=hati-5hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati+hatj-hatk) .

Find the equation of the line perpendicular to the lines : vecr=(3hati+2hatj-4hatk)+lambda(hati+2hatj-2hatk) and vecr=(5hatj-2hatk)+mu(3hati+2hatj+6hatk) and passing through the point (1,1,1)

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 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) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the vector equation of the following planes in scalar product for...

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  2. Find the shortest distance between the following lines whose vector eq...

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  3. Find the vector equation of the following plane in scalar product form...

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  4. Find the equation satisfied by the coordinates of a variable point P(x...

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

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  6. Prove that the normal to the plane containing three point whose positi...

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  7. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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  8. Show that the plane whose vector equation is vecr.(hati+2hatj-hatk)=3 ...

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  9. Find the equation of the plane through the points (2,2,-1) and (3,4,2)...

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  10. Find the equation of the plane which passes through the line (x-3)/2=(...

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  11. Find the equation of the plane containing the line (x-3)/7=(y-4)/0=(z-...

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  12. Find the equation of the plane containing the line (x+1)/-3=(y-3)/2=(z...

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  13. Find the equation of the plane passing through the point (1,1,1) and c...

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  14. Find the equation of the plane which is parallel to the line (x-4)/1=(...

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  15. Find the equation of the plane parallel to the line (x-2)/1=(y-1)/3=(z...

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  16. Evaluate int dx/(secx + tanx)

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  17. Find the equation of the line passing through (1,2,3) and parallel to ...

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  18. Find the equation of the plane, which contains two lines: (x-4)/1=(y-3...

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  19. Find the equation of the plane containingg the lines: vecr=hati+hatj+l...

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  20. Find the vector equation of the line (x-1)/2=(y-2)/-3=(z+3)/4.

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