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Let vec aa n d vec b be mutually perpen...

Let ` vec aa n d vec b` be mutually perpendicular unit vectors. Then for any arbitrary ` vec r ,` a. ` vec r=( vec r . hat a) hat a+( vec r . hat b) hat b+( vec r .( hat axx hat b))( hat axx hat b)` b. ` vec r=( vec r . hat a)-( vec r . hat b) hat b-( vec r .( hat axx hat b))( hat axx hat b)` c. ` vec r=( vec r . hat a) hat a-( vec r . hat b) hat b+( vec r .( hat axx hat b))( hat axx hat b)` d.none of these

A

`vecr= (vecr.hata)hata+(vecr.hatb)hatb+(vecr.(vecaxxhatb)) (hataxxhatb)`

B

`vecr= (vecr.hata)-(vecr.hatb)hatb-(vecr.(vecaxxhatb)) (hataxxhatb)`

C

`vecr= (vecr.hata)hata-(vecr.hatb)hatb-(vecr.(vecaxxhatb)) (hataxxhatb)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `vecr =x_(1) hata+x_(2)hatb +x_(3) (hata xx hatb) `
` Rightarrow vecr.hata =x_(1) +x_(2) hata.hatb + x_(3) hata, (hata xx hatb) =x_(1)`
Also ` vecr.hatb =x_(1) hata.hatb +x_(1)hata.hatb + x_(2) +x_(3) hatb.(hata +hatb) =x_(2)`
`and vecr. (hata xx hat) = x_(1) hata. (hata xx hatb) + x_(2) hatb . (hata xx hatb)`
` =x_(3) (hata xxhatb) . (hata xxhatb) = x_(3)`
` Rightarrow vecr . (hatr.hata ) hata + (vecr . hatb) hatb + ( vecr. (hata xx hatb) ) (hata xx hatb)`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec...

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  3. Let vec aa n d vec b be mutually perpendicular unit vectors. Then f...

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  4. Let veca and vecb be unit vectors that are perpendicular to each other...

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  5. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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  6. Then for any arbitary vector veca, (((veca xx vecb) + (veca xx vecb))...

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  7. If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

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  8. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  9. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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  10. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  11. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y...

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  12. If veca and vecb are two unit vectors inclined at an angle pi//3 then ...

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  13. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  14. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  15. Sholve the simultasneous vector equations for vecx aedn vecy: vecx+vec...

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  16. The condition for equations vec rxx vec a= vec ba n d vec rxx vec c...

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  17. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

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  18. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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  19. Let (veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati...

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  20. For any vectors veca and vecb, (veca xx hati) + (vecb xx hati) + ( vec...

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