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The scalars l and m such that l vec a+m...

The scalars `l` and `m` such that `l vec a+m vec b= vec c` ,where `vec a , vec b` and ` vec c` are given vectors, are equal to

A

`l= ((veccxxvecb).(vecaxxvecb))/((vecaxxvecb)^(2))`

B

`l = ((vecc xx veca). (vecb xxveca))/((vecbxxveca))`

C

`m = ((veccxx veca). (vecbxxveca))/((vecb xx veca)^(2))`

D

`m = ((veccxx veca). (vecbxxveca))/((vecb xx veca))`

Text Solution

Verified by Experts

The correct Answer is:
a,c
Here, ` (l veca +mvecb) xx vecb =vecc xx vecb `
`or lveca xx vecb =vcec xx vecb`
`or l(veca xx vecb)^(2) = (vecc xx vecb) / (veca xx vecb)`
`or l= ((vecc xx vecb) . (veca xx vecb))/ ((veca xx vecb)^(2))`
similarly, `m = ((veccxxveca). (vecb xx veca))/((vecbxxveca)^(2))`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  2. The angles of triangle, two of whose sides are represented by vector...

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  3. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector ...

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  4. If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc...

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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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  20. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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