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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. If vecA=(1,1,1) and vecC=(0,1,-1) are given vectors then find a vector...

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  2. Let vecb=4hati+3hatj and vecc be two vectors perpendicular to each oth...

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  3. The components of a vector veca along and perpendicular to a non-zero ...

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  4. A unit vector coplanar with veci + vecj + 2veck and veci + 2 vecj + ve...

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  5. A non vector veca is parallel to the line of intersection of the plane...

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  6. If vecb and vecc are any two mutually perpendicular unit vectors and v...

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  7. Let veca, vecb and vecc be three vectors having magnitudes 1,1 and 2 r...

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

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

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  10. If veca = hatj + sqrt3hatk = - hatj + sqrt3 hatk and vecc = 2sqrt3 hat...

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

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

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

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  17. If veca and vecb are vectors in space given by veca= (hati-2hatj)/sqrt...

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  18. Let veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk be...

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  19. If veca, vecb and vecc are unit vectors satisfying |veca-vecb|^(2)+|ve...

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  20. Let vec a, vec b, and vec c be three non coplanar unit vectors such th...

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