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Find the Cartesian form of equation of a plane whose vector equation is : ` vec rdot((12 hat i-3 hat j+4 hat k)+5=0`

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Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((- hat i+ hat j+2 hat k)=9

Find the Cartesian form of the equation of the following plane: vec r=( hat i- hat j)+s( hat i+ hat j+2 hat k)+t( hat i+2 hat j+ hat k)dot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=3 hat i+8 hat j+3 hat k+lambda(3 hat i- hat j+ hat k)a n d\ vec r=-3 hat i-7 hat j+6 hat k+mu(-3 hat i+2 hat j+4 hat k)

Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-7 hat k)+lambda( hat i+3 hat j+4 hat k) is parallel to the plane whose vector equation is vec rdot( hat i+ hat j- hat k)=7 . Also find the distance between them.

Find the equation of a plane through the intersection of the planes vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3 and passing through the point (2,1,-2)dot

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.

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

Find the angle between the planes whose vector equations are vec r.(2 hat i+2 hat j-3 hat k)=5 and vec r.(3 hat i-3 hat j+5 hat k)=3 .

Find the Cartesian as well as vector equations of the planes through the intersection of the planes vec rdot((2 hat i+6 hat j)+12=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0 which are at a unit distance from the origin.

RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the angles at which the normal vector to the plane 4x+8y+z=5 is i...

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  2. Find the vector equation of a plane passing through a point having ...

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  3. Find the Cartesian form of equation of a plane whose vector equation i...

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  4. Find the Cartesian form of equation of a plane whose vector equation i...

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  5. Find the vector equations of the coordinates planes.

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  6. Find the vector equation of each one of following plane: 2x-y+2z=8

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  7. Find the vector equation of each one of following plane: x+y-z=5

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  8. Find the vector equation of each one of following plane: x+y=3

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  9. Find the vector and Cartesian equations of a plane passing through the...

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  10. If vec n is a vector of magnitude sqrt(3) and is equally inclined wit...

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  11. The coordinate of the foot of the perpendicular drawn from  the origin...

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  12. Find the equation of the plane passing through the point (2,3,1) ha...

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  13. If the axes are rectangular and P is the point (2, 3, -1), find the eq...

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  14. Find the intercepts made on the coordinate axes by the plane 2x+y-2z=3...

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  15. Find the equation of the plane that bisects the line segment joining ...

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  16. Show that the normal to the following planes are perpendicular to each...

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  17. Show that the normal to the following planes are perpendicular to each...

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  18. Show that the equation of the planes are perpendicular to each other. ...

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  19. Show that the normal vector to the plane 2x+2y+2z=3 is equally incline...

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  20. Find a vector of magnitude 26 units normal to the plane 12 x-3y+4z=1.

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