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If veca and vecb are two unit vectors pe...

If `veca and vecb` are two unit vectors perpenicualar to each other and `vecc= lambda_(1)veca+ lambda_2 vecb+ lambda_(3)(vecaxx vecb),` then which of the following is (are) true ?

A

`lambda_(1)= veca.vecc`

B

`lambda_(2)= |vecb xx vecc|`

C

`lambda_(3)= |(vecaxx vecb|xxvecc|`

D

`lambda_(1)veca + lambda_(2) vecb + lambda_(3) (vecaxxvecb)`

Text Solution

Verified by Experts

The correct Answer is:
a,d
Given `vecc= lambda_(1)veca+lambda_(2)vecb + lambda_(3)(vecaxxvecb)`
`and veca. vecc= lambda_(1),vecc.vecb=lambda_(2)`
` and vecc. (veca xx vecb) |veca xx vecb|^(2) lambda_(3)`
` (1.1 sin 90^(@))^(2) lambda_(3) = lambda_(3)`
Hence, ` lambda_(1), + lambda_(2), + lambda_(3) = (veca + vecb + veca xx vecb) . vecc`
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CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  2. If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ ...

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  3. If veca and vecb are two unit vectors perpenicualar to each other and ...

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  4. If vectors veca and vecb are non collinear then veca/(|veca|)+vecb/(|v...

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  5. If veca and vecb are non - zero vectors such that |veca + vecb| = |vec...

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  6. Let veca vecb and vecc be non- zero vectors aned vecV(1) =veca xx (vec...

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  7. Vectors vecA and vecB satisfying the vector equation vecA+ vecB = vec...

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

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  9. Vectors Perpendicular to hati - hatj- hatk and in the plane of hati + ...

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  10. if side vec(AB) of an equilateral triangle ABC lying in the x-y plane ...

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  11. The angles of a triangle , two of whose sides are respresented by vect...

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  12. veca ,vecb and vecc are unimodular and coplanar. A unit vector vecd is...

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

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  14. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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

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

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  17. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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

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  19. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to (a)[veca...

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  20. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

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