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Find the vector and Cartesian form of th...

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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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)

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

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

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) .

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

The vector equation of the line passing through the points (3,5, 4) and (5, 8, 11) is vecr=3hati+5hatj+4hatk+lamda(2hati+3hatj+7hatk)

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

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6.

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

ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 6 MARKS:
  1. Find image of point (1, 3, 4) in the plane 2x-y+z+3=0.

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  2. Find the distance between the point (7,2,4) and the plane determined b...

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  3. Find the distance between the point P(6,5,9) and the plane determined ...

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  4. Find the cartesian and vector equations of the planes passing through ...

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  5. Find the co-ordinates of the points where the line through the points ...

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  6. Find the coordinates of the point where the line through the points A ...

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  7. Find the distance of the point (3,4,5) from the plane x+y+z=2 measured...

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  8. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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

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

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

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  12. Find the value of k for which the following lines are perpendicular to...

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  13. Find the equation of the plane passing through the points (2,1,0), (3,...

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  14. Find the vector and Cartesian form of the equation of the plane passin...

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  15. The lines x+3y-1=0 and x-4y=0 intersect each other. Find their point o...

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  16. Show that the lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) ...

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  17. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  18. Let P(3, 2, 6) be a point in space and Q be a point on the line r=(ha...

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  19. Find the equation of the plane passing through the point A(1, 2, 1) an...

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

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