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Show that (veca-vecb)xx(veca+vecb)=2veca...

Show that `(veca-vecb)xx(veca+vecb)=2vecaxx vecb` and give a genometrical interpretation of it.

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`(veca - vecb) xx (veca + vecb) `
`= vecaxxveca + vecaxxvecb -vecbxxveca -vecbxxvecb`
`= veca xx veca + veca xx vecb + veca xx vecb -vecb xx vecb`
`= vec0 + 2veca xx vecb - vec0 = 2vea xx vecb`
Geometrically, the vector area of a parallelogram, whose sides are along vectors, `veca and vecb is veca xx vecb`. Also diagonals are long vectors, `veca - vecb and veca + vecb` and the vector area in terms of diagonal vectors is
`1/2 [(veca -vecb) xx (veca + vecb)]`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. I the vectors veca,veca=xhati+yhatj+zhatka and vecb=hatj are such that...

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  2. given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca...

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  3. Show that (veca-vecb)xx(veca+vecb)=2vecaxx vecb and give a genometrica...

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  4. If vec x and vecy are unit vectors and |vecz| = 2/sqrt7 such that vecz...

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  5. prove that (veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)...

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  6. Let veca vecb and vecc be three non-zero vectors such that veca + vecb...

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  7. A particle has an angular speed of 3 rad/s and the axis of rotation...

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  8. Let vea, vecb and vecc be unit vectors such that veca.vecb=0 = veca.ve...

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  9. If |vecaxxvecb|^(2)+(veca.vecb)^(2)=144and|veca|=4,"then "|vecb| is eq...

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  10. Given |veca|=|vecb|=1 and |veca + vecb|= sqrt3 "if" vecc is a vector s...

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  11. Find the moment of vec F about point (2, -1, 3), where force vec ...

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  12. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

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  13. If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm ...

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  14. if the volume of a parallelpiped whose adjacent egges are veca=2hati+3...

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  15. If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector vec...

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

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  17. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

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  18. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

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  19. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. Vecb =0 then prove...

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  20. prove that (veca.(vecbxxhati)hati(veca.(vecbxxhatj))hatj+ (veca.(vecbx...

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