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for any three vectors, veca, vecb and ve...

for any three vectors, `veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc`.

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Clearly, vectors `veca - vecb, vecb-vecc, vecc-veca` are coplanar,
`Rightarrow [ veca -vecb vecb- vecc vecc-veca] =0`
Therefore, the given statement is false.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let vecA, vecB and vecC be unit vectors such that vecA.vecB = vecA.vec...

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  2. If vecx.veca=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector vec...

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  3. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  4. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

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  5. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vec|=|veca||vecb|...

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  6. The volume of he parallelepiped whose sides are given by vec O A=2...

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  7. Let veda,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

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  8. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  9. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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  10. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

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  11. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  12. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  13. Let veca = 2i + j -2k, and b = i+ j if c is a vector such that veca ....

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  14. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  15. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  16. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

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  17. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  18. if hata, hatb and hatc are unit vectors. Then |hata - hatb|^(2) + |hat...

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  19. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  20. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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