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If vectors vec A=2 hat i+3 hat j+4 hat ...

If vectors ` vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat k` and `vec C` form a left-handed system, then ` vec C` is a.`11 hat i-6 hat j- hat k` b.`-11 hat i+6 hat j+ hat k` c. `11 hat i-6 hat j+ hat k` d. `-11 hat i+6 hat j- hat k`

A

`11 hati - 6 hatj - hatk`

B

`-11 hati - 6 hatj - hatk`

C

`-11 hati - 6 hatj + hatk`

D

`-11 hati + 6 hatj - hatk`

Text Solution

Verified by Experts

The correct Answer is:
b,d
For `vecA, vecB and vecC` to form a left- handed system
`[vecA vecB vecC] lt 0`
`vecA xx vecV=|{:(hati,hatj,hatk),(2,3,4),(1,1,5):}|=11hati -6hatj-hatk`
(i) is satisfied by options (b) and (d)
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  5. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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  6. if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 ...

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  7. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  8. If vec a , vec b , a n d harr c are three unit vecrtors such that ...

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  9. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  10. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  11. The scalars l and m such that l vec a+m vec b= vec c ,where vec a , v...

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  12. If (veca xx vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of ...

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  13. A ,B ,Ca n dD are four points such that vec A B=m(2 hat i-6 hat j+2 h...

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  14. If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are dist...

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  15. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  16. If vectors vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat ...

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  17. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

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  18. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

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  19. A vector (vecd) is equally inclined to three vectors veca= hati - hatj...

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