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A tetrahedron is three dimensional figur...

A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates `(x_(1),y_(1),z_(1)) (x_(2), y_(2), z_(2)) , (x _(3), y_(3) , z_(3)) and (x _(4), y _(4), z _(4))` respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are
`((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)).`
The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron.
Let tetrahedron has three of its vertices represented by the points
`(0,0,0) ,(6,-5,-1) and (-4,1,3)` and its centroid lies at the point `(1,-2,5).` Now answer the following questions
The distance between the planes `x + 2y- 3z -4 =0 and 2x + 4y - 6z=1` along the line `x/1= (y)/(-3) = z/2` is :

A

`19/22`

B

`(7 sqrt7)/(22)`

C

`(7)/(22)`

D

`(7 sqrt14)/(22)`

Text Solution

Verified by Experts

The correct Answer is:
D
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A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (x_(1),y_(1),z_(1)) (x_(2), y_(2), z_(2)) , (x _(3), y_(3) , z_(3)) and (x _(4), y _(4), z _(4)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The coordinate of the fourth vertex of the tetrahedron is :

A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (x_(1),y_(1),z_(1)) (x_(2), y_(2), z_(2)) , (x _(3), y_(3) , z_(3)) and (x _(4), y _(4), z _(4)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The equation of the triangular plane of tetrahedron that contains the given vertices is :

A tetrahedron is a three dimensional figure bounded by four non coplanar triangular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates (x_1,y_1,z_1)(x_2,y_2,z_2),(x_3,y_3,z_3) and (x_4,y_4,z_4) respectively in a rectangular three dimensional space. Then the coordinates of its centroid are ((x_1+x_2+x_3+x_3+x_4)/4, (y_1+y_2+y_3+y_3+y_4)/4, (z_1+z_2+z_3+z_3+z_4)/4) . the circumcentre of the tetrahedron is the center of a sphere passing through its vertices. So, this is a point equidistant from each of the vertices of the tetrahedron. Let a tetrahedron have three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,2,5). The coordinate of the fourth vertex of the tetrahedron is

A tetahedron is a three dimensional figure bounded by forunon coplanar trianglular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates (x_1,y_1,z_1)(x_2,y_2,zs_2),(x_3,y_3,z_3) and (x_4,y_4,z_4) respectivley in a rectngular three dimensionl space. Then the coordinates of tis centroid are (x_1+x_2+x_3+x4)/4, (y_1+y_2+y_3+y_4)/4, (z_1+z_2+z_3+z_4)/4 . the circumcentre of the tetrahedron is th centre of a sphere pssing thorugh its vetices. So, this is a point equidistasnt from each ofhate vertices fo the tetrahedron. Let a tetrahedron hve three of its vertices reresented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centrod lies at the point (1,2,5). THe coordinate of the fourth vertex of the tetrahedron is

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VMC MODULES ENGLISH-THREE DIMENSIONAL GEOMETRY -LEVEL-1
  1. A tetrahedron is three dimensional figure bounded by four non coplanar...

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  2. A tetrahedron is three dimensional figure bounded by four non coplanar...

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  3. A tetrahedron is three dimensional figure bounded by four non coplanar...

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  4. Find the perpendicular distance of an angular point of a cube from a d...

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  5. The plane passing through the point (-2, -2, 2) and containing the lin...

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  6. The equation of the plane contaiing the lines vecr=veca(1)+lamda vecb ...

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  7. Lines vecr = veca(1) + lambda vecb and vecr = veca(2) + svecb will lie...

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  8. The symmetric form of the equation of the line x + y-z =3, 2x+3y+ z+4=...

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  9. Which of the statement is true? The coordinate planes divide the line ...

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  10. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

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  11. The equation of the plane through the point (2,5,-3) perpendicular to...

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  12. The equation of the plane passing through the points (3,2,-1) , (3,4,...

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  13. The linee joining the points (1,1,2) and (3,-2,1) meets the plane 3x+2...

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  14. The equation of the plane through the point (0,-4,-6) and (-2,9,3) and...

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  15. What are corrdinates of the point equidistant from the points (a,0,0),...

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  16. The intercepts made on the axes by the plane the which bisects the ...

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  17. The plane passing through the point (5,1,2) perpendicular to the line ...

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  18. The lines (x+1)/(1)=(y-1)/(2)=(z-2)/(1),(x-1)/(2)=(y)/(1)=(z+1)/(4) ar...

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  19. The coordinates of the centriod of triangle ABC where A,B,C are the p...

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  20. What is the equation of the plane which passes through the z-axis and ...

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