Home
Class 12
MATHS
The volme of a tetrahedron having vertic...

The volme of a tetrahedron having vertices `A(1,1,1),B(1,2,4),C(3,1,-2)` and `D(4,3,1)` is `x` cubic unit then `2x=`

Text Solution

AI Generated Solution

To find the volume of the tetrahedron with vertices \( A(1,1,1) \), \( B(1,2,4) \), \( C(3,1,-2) \), and \( D(4,3,1) \), we can use the formula for the volume of a tetrahedron given by: \[ V = \frac{1}{6} \left| \vec{AB} \cdot (\vec{AC} \times \vec{AD}) \right| \] ### Step 1: Calculate the vectors \( \vec{AB} \), \( \vec{AC} \), and \( \vec{AD} \) ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise MATHEMATICS|259 Videos

Similar Questions

Explore conceptually related problems

area of the triangle with vertices A(3,4,-1), B(2,2,1) and C(3,4,-3) is :

Find the area of the triangle whose vertices are A(3,-1,2),\ B(1,-1,-3)a n d\ C(4,-3,1)dot

The area of the triangle having vertices P(1,2,3),Q(4,0,4),R(-2,4,2) is (A) 5 units (B) 10 units (C) 4 units (D) none of these

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1) and C(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)

Consider a tetrahedron D-ABC with position vectors if its angular points as A(1, 1, 1), B(1, 2, 3), C(1, 1, 2) and centre of tetrahedron ((3)/(2), (3)/(4),2) . Q. If N be the foot of the perpendicular from point D on the plane face ABC then the position vector of N are :

Consider a tetrahedron D-ABC with position vectors if its angular points as A(1, 1, 1), B(1, 2, 3), C(1, 1, 2) and centre of tetrahedron ((3)/(2), (3)/(4),2) . Q. If N be the foot of the perpendicular from point D on the plane face ABC then the position vector of N are :

Consider a tetrahedron D-ABC with position vectors if its angular points as A(1, 1, 1), B(1, 2, 3), C(1, 1, 2) and centre of tetrahedron ((3)/(2), (3)/(4),2) . Q. Shortest distance between the skew lines AB and CD :

Consider a tetrahedron D-ABC with position vectors if its angular points as A(1, 1, 1), B(1, 2, 3), C(1, 1, 2) and centre of tetrahedron ((3)/(2), (3)/(4),2) . Q. Shortest distance between the skew lines AB and CD :