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If veca=hati+hatj + hatk and vecb = hati...

If `veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk` then find the vector `vecc` such that `veca.vecc =2 and veca xx vecc=vecb`.

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`vecaxxvecb =veca xx (vecaxxvecc) = (veca .vecc)veca-(veca.veca)vecc= 2veca -3vecc`
`vecaxx vecb= |{:(pi,j,k),(1,1,1),(1,-2,1):}|=3hati-3hatk`
`vecc = 1/3 (2veca -vecaxxvecb) = 1/3 (-hati + 2hatj + 5hatk)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector 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. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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