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If vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)...

If `vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)+v(vecwxxvecu) and [vecu vecv vecw]=1/5 then lamda +mu+v=` (A) 5 (B) 10 (C) 15 (D) none of these

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The correct Answer is:
6
q= Area of parallelogram with `vec(OA) and vec(OC)` as adjacent sides
`|vec(OA) xx vec(OC)|`
`|veca xx vecb|`
p = Area of quadrilateral OABC
`1/2|vec(OA)xx vec(OB)|+1/2|vec(OB)xx vec(OC)|`
`1/2[|veca xx(10 veca + 2vecb)|+|(10veca + 2vecb)xxvecb|]`
`1/2|(12veca xx vecb)|=6|veca xx vecb| Rightarrow k =6`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let veca, vecb and vecc be three vectors having magnitudes 1,1 and 2 r...

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  2. A, B C and D are four points in a plane with position vectors, veca, v...

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  3. If vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)+v(vecwxxvecu) and [vecu vecv ...

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  4. If veca = hatj + sqrt3hatk vecb= - hatj + sqrt3 hatk and vecc = 2sqrt3...

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  5. Let vecA, vecB and vecC be unit vectors such that vecA.vecB = vecA.vec...

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  6. If vecx.veca=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector vec...

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  7. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  8. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

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  9. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vec|=|veca||vecb|...

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  10. The volume of he parallelepiped whose sides are given by vec O A=2...

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  11. Let veda,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

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  12. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  13. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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  14. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

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  15. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  16. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  17. Let veca = 2i + j -2k, and b = i+ j if c is a vector such that veca ....

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  18. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  19. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  20. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

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