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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. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

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  2. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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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).vecc|=|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. If veca , vecb , vecc are three non-coplanar vector and vecp...

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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, vecc are three non - coplanar vector such that vecaxx(v...

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  10. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. 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. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  13. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  14. Let vec a=2i+j+k , vec b=i+2j-k and a unit vector vec c be coplanar....

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

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  16. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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

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  18. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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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 vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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