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

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