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for any four vectors veca,vecb, vecc and...

for any four vectors `veca,vecb, vecc and vecd` prove that `vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]`

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`vecd.(vecaxx(vecbxx (vecc xxvecd)))`
`= vecd.(vecaxx((vecb.vecd)vecc- (vecb.vecc)vecd)))`
`vecd. ((vecb.vecd)(veca xx vecc)- (vecb.vecc)(veca xxvecd))`
`=(vecb.vecd)(vecd.(vecaxxvecc))-(vecb.vecc)(vecd.(veca xx vecd))`
`(vecb.vecd) [vecdvecavecc]`
`(vecb.vecd) [veca vecc vecd]`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. Vecb =0 then prove...

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

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  3. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

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  4. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

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  5. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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  6. Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)x...

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  7. If vecp, vecq , vecr denote vectors vecbxxvecc, vecc xx vecc xx veca, ...

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  8. Let veca, vecb , vecc be non -coplanar vectors and let equations veca'...

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  9. Given unit vectors hatm hatn and hatp such that angle between hatm and...

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  10. vec a , vec b ,a n d vec c are three unit vectors and every two are...

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  11. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati + b(2)hatj + b(3)hat...

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  12. If |{:((a-x)^(2),(a-y)^(2),(a-z)^(2)),((b-x)^(2),(b-y)^(2),(b-z)^(2)),...

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  13. OABC is a tetrahedron where O is the origin and A,B,C have position ve...

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  14. Let k be the length of any edge of a regular tetrahedron (a tetrahe...

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  15. In A B C , a point P is taken on A B such that A P//B P=1//3 and poin...

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  16. Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + ...

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  17. The lengths of two opposite edges of a tetrahedron of aa n db ; the...

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  18. Find the volume of a parallelopiped having three coterminus vectors of...

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  19. Let vecp and vecq any two othogonal vectors of equal magnitude 4 each....

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  20. Given that vecA,vecB,vecC form triangle such that vecA=vecB+vecC. Find...

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