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Show that, if the axes are rectangular, the equations of the line through `(x_1, y_1, z_1)` at right angles to the lines: `x/l_1=y/m_1=z/n_1,x/l_2=y/m_2=z/n_2` are `frac{x-x_1}{m_1n_2-m_2n_1}=frac{y-y_1}{n_1l_2-n_2l_1}=frac{z-z_1}{l_1m_2-l_2m_1}`

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equations of the straight line passing through the point (1, ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Determine whether or not the following paris of lines intersect: vecr=...

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