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The volume (in cubic unit) of the tetrah...

The volume (in cubic unit) of the tetrahedron with edges `hati+hatj+hatk, hati-hatj+hatk and hati-2hatj-hatk` is

A

4

B

`2//3`

C

`1//6`

D

`1//3`

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The correct Answer is:
B
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SIA PUBLICATION-ADDITION OF VECTORS AND PRODUCT OF VECTORS-Problems
  1. The ratio in which i + 2j + 3k divides the join of -2i + 3j + 5k and 7...

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  2. If veca=overset(-)i-overset(-)j-overset(-)k and vecb=lambda hati-3hatj...

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  3. The volume (in cubic unit) of the tetrahedron with edges hati+hatj+hat...

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  4. If a + b + c = 0 and |a| = 3, |b| = 4 and |c| = sqrt(37) the angle bet...

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  5. The position vector of a point lying on the line joining the points wh...

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  6. If hati-2hatj,3hatj+4hatk and lambda hati+3hatj are coplanar, then lam...

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  7. If the volume of parallelopiped with conterminus edges 4hati+5hatj+hat...

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  8. If veca. hati+veca. (2hati+hatj)=veca. (hati+hatj+3hatk)=1 then veca i...

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  9. If the vector veca=2hati+3hatj+6hatk and vecb are collinear and |vecb|...

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  10. If vec(a) and vec(b) are unit vectors, then the vectors (vec(a) + vec(...

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  11. Statement I Two non-zero, non-collinear vectors are linearly independe...

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  12. Match the columns and choose the correct answer.

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  13. Assertion (A): Three vectors are coplanar if one of them is expressibl...

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  14. The points collinear (1,-2,-3) and (2,0,0) among the following is

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  15. If hati+2hatj+3hatk, 3hati+2hatj+hatk are the sides of a parallelogram...

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  16. If G is the centroid of the triangleABC," then "overset(-)(GA)+overset...

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  17. if the vectors hati+3hatj+4hatk, lambda hati-4hatj+hatk are othogonal ...

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  18. The vector vecc. (vecb+vecc) xx (veca +vecb+vecc) is equal to

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  19. If 3hati+3hatj+sqrt3hatk, hati+hatk, sqrt3 hati+sqrt3 hatj+lambda hatk...

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  20. If D,E and F are respectively the mid points of AB, AC and BC in trian...

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