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Show that the lines: `vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk)` are intersecting. Hence find their point of intersection.

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Show that the lines: vecr=(hati+hatj)+lambda(2hati-hatk) and vecr=(2hati-hatj)+mu(hati+hatk-hatk) do not intersect.

Check whether the lines vecr=hati+hatj-hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+hatk) intersect or not.

Show that the lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk) are intersecting. Hence, find their point of intersection.

Show that the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk)and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk) are intersecting. Also, find the point of intersection.

Find whether the lines: vecr=(hati-hatj-hatk)+lambda(2hati+hatj) and vecr=(2hati-hatj)+mu (hati+hatj-hatk) intersect or not. If itersecting, find their point of intersection..

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

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

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

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the equations the lines joining the following pair of vertices: (...

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  2. Find the shortest distance between the lines ((x+1)/7=(y+1)/-6=(z+1)/1...

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  3. Show that the lines: vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr...

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  4. Find the equation of the plane with the intercept 5 on the y axis and ...

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  5. Find the equation of the plane with intercept 4 on the z axis and para...

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  6. Find the vector equation of a plane, which is at a distance of 7 uits ...

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  7. Find the vector equation of a plane, which is at a distance of 5 units...

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  8. Find the vector equation of the plane whose cartesian form of equation...

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  9. Find the vector equation of the plane whose cartesian form of equation...

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  10. Find the cartesian equations of the following planes: vecr*(3hati+3hat...

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  11. Find the cartesian equations of the following planes: vecr*(2hati+3hat...

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  12. Find the Cartesian equation of the following plane: vecr cdot [(s-2t)h...

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  13. What are the direction cosines of the normal to the plane 3x+2y-3z=8?

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  14. Find the direction cosine of the perpendicular from origin to plane ve...

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  15. Find the vector equation of the line through the origin, which is perp...

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  16. Find the distance of the points (2,3,4) from the plane vec(R)*(3hat(i)...

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  17. Find the distance of a point (2,5,-3) from the plane vec(R)*(6hat(i)-3...

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  18. Find the distance from (1,2,3) to the plane 2x+3y-z+2=0

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  19. Find the length of the perpendicular drawn from the origin to the plan...

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  20. Find a unit vector normal to the plane : vecr*(2hati-3hatj+6hatk)+14=0...

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