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Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines `vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk)`.

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

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Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

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Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

Find the angle between the lines vecr=2hati+3hatj-4hatk+lambda(2hati+1hatj+2hatk) and vecr=2hati-5hatk+mu(6hati+3hatj+2hatk)

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the length and foot of perpendicular drawn from the point (2,-1,3...

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  2. Find the equations of the straight line passing through the point (1, ...

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  3. Find the equation in vector anf cartesian form of the line passing thr...

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  4. Show that, if the axes are rectangular, the equations of the line thro...

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  5. Find the coordinates of the foot of the perpendicular drawn from point...

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  6. A(1,0,4), B(0,-11,3), C(2,-3,1) are three points and D is the foot of ...

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  7. Find the equation of the line joining the points A(0,-1,3) and B(2,-3,...

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  8. Find the vector equation of the line joining the points A(1,-1,2) and ...

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  9. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

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  10. A line makes angles alpha, beta, gamma, delta with the diagonals of a ...

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  11. If the edges of a rectangular parallelopiped are a, b and c, show that...

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  12. Find the general solution of the following (1+sinx)dy=ydx

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  13. Prove that the two lines whose direction cosines are connected by the ...

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  14. Find the general solution of the following (1+secx)dy=y^2dx

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  15. Find the shortest distance between two lines whose vector equations ar...

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  16. Find the shortest distance between each of the following pair of lines...

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  17. Find the shortest distance between each of the following pair of lines...

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  18. Find the general solution of the following (sinx+cosx)dy=y(cosx-sinx)d...

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  19. Find the shortest distance between each of the following pair of lines...

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  20. Find shortest distance between lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)...

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