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Prove that the volume of the tetrahedron...

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of `27:1.`

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27
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MCGROW HILL PUBLICATION-VECTOR ALGEBRA-SOLVED EXAMPLES (Numerical Answer Type Questions)
  1. Let the position vectors of vertices of a DeltaABC be OA=3i+j+2k, OB=i...

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  2. Suppose 4i+7j+8k, 2i+3j+4k, 2i+5j+7k are respectively the position vec...

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  3. Prove that the volume of the tetrahedron and that formed by the centro...

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  4. bar a=2 bar i+bar j-2bar k and bar b=bar i+bar j if bar c is a vecto...

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  5. Suppose a and b are two unit vectors and theta is acute angle between ...

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  6. The vector a, b and c are such tha |a|=|b| = 1 and |c|= 2 (ii) a ...

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  7. Let a=2i-3j+4k, b=i+2j-2k " and "c=3i-j+k. Let V be, the volume (in cu...

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  8. If A(3i-2j-k), B(2i+3j-4k), C(-i+j+2k)" and "D(4i+5j+lambdak) are copl...

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  9. Suppose a+x^(2)b+y^(2)c=0" and "a times b+c times a=16(b times c), the...

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  10. Let veca,vecb and vecc be three vectors having magnitudes 1, 1 and 2 r...

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  11. Suppose ABC is a right angled triangle with angleC=pi//2. If abs(AB)=5...

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  12. Let a=5i+4j-k, b=-4i+j+5k, c=i+3j-k. Let alpha be a vector perpendicul...

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  13. If the volume of parallelopiped whose coterminous edges are a=i+j+2k, ...

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  14. Suppose P=(x+1)i+xj+xk, Q=x""i+(x+1)j+xk, k=x""i+xj+(x+1)k are coplana...

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  15. Let abs(a)=sqrt(3), abs(b)=5, b*c=10, angle between b and c is equal t...

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  16. Let a,b,c be three vectors such that a ne 0 and a xx b = 2a xx c,|a|...

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  17. Let a=i-2j+3k. If b is a vector such that a*b=abs(b)^(2)" and "abs(a-b...

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  18. Suppose the diagonals of a parallelogram are represented by vectors i+...

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  19. Let a be vector, such that abs(a)=5. Then abs(a*i)^(2)+abs(a*j)^(2)+ab...

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  20. If vecr=l(vecb xx vecc)+m(vecc xx veca)+n(veca xx vec b) and [veca, v...

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