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Find cartesian equations of the plane containing the lines: `vecr=2hati+hatj-3hatk+lambda(hati+2hatj+5hatk)` and `vecr=3hati+3hatj-7hatk+mu(3hati-2hatj+5hatk)`

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Find the vector and cartesian equations of the plane containing the lines: vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(-2hati+3hatj+8hatk) .

Find the angle between the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=8hati-2hatj+mu(3hati+2hatj+5hatk) .

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 shrotest distance between the lines vecr=hati-7hatj-2hatk+lamda(hati+3hatj+2hatk) and vecr=3hati+4hatj-2hatk+mu(-hati+2hatj+hatk)

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

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

Find the shortest distance between the lines: vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk) .

find the shortest distance between the lines vecr=6hati-hatj+3hatk+lambda(hati+3hatj+2hatk) and hatr=9hati+hatj-4hatk+mu(hati-2hatj+hatk)

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

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the vector equation of the line passing through (1, 2, 3) and per...

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  2. Find the equation of the plane passing through (a, b, c) and parallel ...

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  3. Find cartesian equations of the plane containing the lines: vecr=2hat...

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  4. Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+...

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  5. Show that the lines : 3x-2y+5=0, y+3z-15=0 and (x-1)/5=(y+5)/-3=z/1 ar...

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  6. Find the equations of the line passing through the point (1,-2,-3) and...

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  7. Find the equation of the plane, which bisects the line joining the poi...

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  8. Find the equation of the plane throught he intersection of the planes ...

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  9. Find the vector equation of the plane through the planes : vecr*(hati+...

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

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  11. Find the Cartesian equation of the plane passing through three non-col...

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  12. Find the equations of the plane that passes through three points : (1,...

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  13. Find the equations of the planes passing through the following points ...

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  14. Find the equation of the plane through three non-collinear points (0, ...

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  15. Find the equation of the plane passing through the points : (3, -1, 2)...

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  16. Find the equation of the plane through three non-collinear points: (2,...

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  17. Find the equation of the plane through three non-collinear points: (2,...

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  18. Find the equation of the plane throught he points (3,-2,4), (-13,17,-1...

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  19. Find the equations of the planes passing through the following points ...

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

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