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Find the equation of the plane through the intersection of the planes `vecr.(bari+3barj)-6=0` and `barr.(3bari-barj-4bark)=0`, whose perpendicular distance from origin is unity.

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Find the cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Find the equation of the plane through the intersection of the planes x+3y+6=0 and 3x-y-4z=0 , whose perpendicular distance from the origin is unity.

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to X- axis.

Find the equation of the plane through the point (1,4,-2) and parallel to the plane -2x+y-3z=7 .

Find the equation of the plane through the line of intersection of vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to vecr.(2hati-hatj+hatk)+8=0

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6 and vecr.(2hati+3hatj+4hatk)=-5 and the points (1,1,1).

Find the equation of the plane which contains the line of intersection of the planes vecr.(hati+2hatj+3hatk)-4=0,vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr.(5hati+3hatj-6hatk)+8=0

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+3hatj-hatk)=0 and vecr.(hatj+2hatk)=0 and also passing through the point 2hati+hatj-hatk .

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
  1. Find the equation of the plane which is perpendicular to the plane 5x ...

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  2. If the plane ax + by = 0 is rotated about its line of intersection wit...

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

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  4. Show that the points bari-barj+3bark and 3(bari +barj+bark) are equidi...

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  5. vec(AB)=3bari-barj+bark and vec(CD)= -3bari+2barj+4bark are two vector...

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  6. Show that the straight lines whose direction cosines are given by 2l +...

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  7. If (l1, m1, n1), (l2, m2, n2)" and "(l3, m3, n3) are the direction cos...

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  8. Distance of the point (alpha,beta,gamma) from Y- axis is …........

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  9. If the directions cosines of a line are k, k and k then ..........

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  10. The distance of the plane barr.(2/7i+3/7j-6/7k)=1 from the origin is …...

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  11. The sine of the angle between the straight line (x-2)/(3)=(y-3)/(4)=(z...

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  12. The reflection of the point (alpha,beta,gamma) in the xy - plane is .....

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  13. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4...

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  14. The locus represented by xy + yz = 0 is .........

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  15. The plane 2x – 3y + 6z - 11 = 0 makes an angle sin^(-1)alpha with X- a...

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  16. A plane passes through the points (2, 0, 0) (0,3,0) and (0, 0, 4). The...

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  17. The direction cosines of the vector 2bari + 2barj - bark are ............

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  18. The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2).Writ...

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  19. The vector equation of the line through the points (3, 4, -7) and (1, ...

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  20. The cartesian equation of the plane barr.(bari+barj-bark)=2 is...........

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