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If ` vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3` are two sets of vectors such that ` vec e_idot vec E_j=1,ifi=ja n d vec e_idot vec E_j=0a n difi!=j ,` then prove that `[ vec e_1 vec e_2 vec e_3][ vec E_1 vec E_2 vec E_3]=1.`

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we know that
`[vece_(1)vece_(2)vece_(3)][vecE_(1) vecE_(2)vecE_(3)]=|{:(vece_(1).vecE_(1),vece_(1).vecE_(2),vece_(1).vecE_(3)),(vece_(2).vecE_(1),vece_(2).vecE_(2),vece_(2).vecE_(2)),(vece_(3).vecE_(1),vece_(3).vecE_(2),vece_(3).vecE_(3)):}|`
`=|{:(1,0,0),(0,1,0),(0,0,1):}|`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Given that vecA,vecB,vecC form triangle such that vecA=vecB+vecC. Find...

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  2. A line l is passing through the point vecb and is parallel to vector v...

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  3. If vec e1, vec e2, vec e3a n d vec E1, vec E2, vec E3 are two sets of...

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  4. In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals A...

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  5. O A B C is regular tetrahedron in which D is the circumcentre of O...

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  6. If A( vec a),B( vec b)a n dC( vec c) are three non-collinear points...

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  7. If veca, vecb, vecc are three given non-coplanar vectors and any arbit...

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  8. Two vectors in space are equal only if they have equal component in...

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  9. Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 an...

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  10. Let veca, vecb , vecc be three vectors of equal magnitude such that t...

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  11. If veca,vecb,vecc are three mutually perpendicular vectors, then the v...

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  12. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  13. If veca and vecb are two vectors, such that veca.vecblt0 and |veca.vec...

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  14. If hata,hatb and hatc are three unit vectors such that hata + hatb + h...

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  15. If veca, vecb,vecc are unit vectors such that veca.vecb = 0= veca.vecc...

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  16. P (vecp) and Q (vecq) are the position vectors of two fixed points and...

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  17. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

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  18. If hata,hatb and hatc are three unit vectors inclined to each other at...

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  19. Let the pair of vector veca,vecb and vecc,veccd each determine a plane...

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  20. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

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