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If veca = (hati + hatj +hatk), veca. vec...

If `veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -hatk , " then " vecb` is (a)`hati - hatj + hatk` (b) `2hati - hatk` (c) `hati` (d) `2hati`

A

`hati-hatj+hatk`

B

`2hatj-hatk`

C

`hati`

D

`2hati`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`vecaxxvecb=hatj-hatk`
`impliesvecaxx(vecaxxvecb)=vecaxx(hath-hatk)`
`implies(veca.vecb)veca-(veca.veca)vecb=(hati+hatj-hatk)xx(hatj-hatk)`
`implies (hati+hatj+hatk)-3vecb=-2hati+hatj+hatkimplies3vecb=3hatiimpliesvecb=hati`
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Section I - Solved Mcqs
  1. If veca, vecb, vecc are any three non coplanar vectors, then (veca+v...

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  2. Let veca, vecb and vecc be three having magnitude 1,1 and 2 respective...

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  3. If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -ha...

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  4. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  5. If the vectors veca, vecb, vecc and vecd are coplanar vectors, then (...

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  6. (vecaxxvecb).(veccxxvecd) is not equal to

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  7. Let veca = 2hati + hatj + hatk, and vecb = hati+ hatj if c is a vecto...

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  8. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  9. The number of faces of a triangular pyramid or tetrahedron is .

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  10. The acute angle that the vector 2hati-2hatj+hatk makes with the plane ...

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  11. If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2...

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  12. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  13. Let G(1), G(2) and G(3) be the centroid of the triangular faces OBC, O...

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  14. Let vecr, veca, vecb and vecc be four non -zero vectors such that vecr...

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  15. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

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  16. If a and b are unit vectors, then the vector defined as V=(a+b)times(a...

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  17. If vec(alpha)=2hati+3hatj-hatk, vec(beta)=-hati+2hatj-4hatk, vecgamma=...

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  18. Let alpha = a hati + b hatj + chatk , vecbeta = bhati + chatj + ahatk ...

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  19. Given |veca|=|vecb|=1 and |veca + vecb|= sqrt3 if vecc is a vector suc...

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  20. If vecmu and vecv be unit vector. If vecv is a vector such that vecv +...

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