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Find the vector equation of the plane wh...

Find the vector equation of the plane which is at a distance of 7 units from the origin and which is normal to the vector `3hat(i)+5hat(j)-6hat(k)`.

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Find the vector equation of a plane which is at a distance of 8 units from the origin and which is normal to the vector 2 hat i+ hat j+2 hat kdot

Find the equation of the line through the point (1,2,0) and is parallel to the vector 2hat(i)+3hat(j)-5hat(k) .

Find the vector equation of plane that passes through the point (1,0,-2) and the normal to the plane is hat(i)+hat(j)-hat(k) .

Find the equation of the plane which contains the line of intersection of the planes vec(r)*(hat(i)+2hat(j)+3hat(k))-4=0,vec(r)*(2hat(i)+hat(j)-hat(k))+5=0 and which is perpendicular to the plane vec(r)*(5hat(i)+3hat(j)-6hat(k))+8=0

Find the vector equation of the plane through the intersection of the planes vec(r)*(hat(i)+hat(j)+hat(k))=6 and vec(r)*(2hat(i)+3hat(j)+4hat(k))=-5 and the point (1,1,1).

The vector equation of the plane through the point 2hat(i)-hat(j)-4hat(k) and parallel to the plane rcdot(4hat(i)-12hat(j)-3hat(k))-7=0 is

Find the vector equation of the plane passing through the intersection of the planes vec(r)*(2hat(i)+2hat(j)-3hat(k))+7=0 and vec(r)*(2hat(i)+5hat(j)+3hat(k))=9 and passing through the point (2,1,3).

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by r=(3hat(i)+8hat(j)+3hat(k))+lambda(3hat(i)-hat(j)+hat(k)) and r=(-3hat(i)-7hat(j)+6hat(k))+mu(-3hat(i)+2hat(j)+4hat(k)) .

Find the equation of the sphere whose centre has the position vector 3hat(i)+6hat(j)-4hat(k) and which touches the plane r*(2hat(i)-2hat(j)-hat(k))=10 .

OMEGA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Questions
  1. Find the shortest distance between the lines ((x+1)/7=(y+1)/-6=(z+1)/1...

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

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  3. Find the vector equation of the plane which is at a distance of 7 unit...

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  4. Find the cartesian equation of plane vec(r)*(hat(i)+hat(j)-hat(k))=2

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  5. Find the co-ordinates of the foot of the perpendicular drawn from the ...

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

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  7. Find the equation of the plane passing through the point ( 1, -1 , 2) ...

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  8. Find the intercepts cut off by the plane 2x+y-z = 5

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  9. Find the vector equation of the plane through the intersection of the ...

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  10. Find the vector equation of plane passing through the intersection of ...

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  11. Find the equation of the plane through the intersection of the planes ...

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  12. Find the equation of the plane passing through the line of intersectio...

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  13. Find the angle between the planes whose vector equations are vec(r)(...

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  14. Find the vector equation of plane that passes through the point (1,0,-...

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  15. If a line has direction ratios -18,12,-4, then what are its direction ...

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  16. Find the direction cosines of the sides of the triangle whose vertices...

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  17. A line passes through the point with position vector 2hat(i)-hat(j)+4h...

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  18. Show that the line through the points : (4,7,8), (2,3,4) is parallel t...

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  19. Find the cartesian equation of the line which passes through the point...

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  20. The vector equation of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is ........

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