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vec(a)=2hati+lambda(1)hatj+3hatk,vec(b)=...

`vec(a)=2hati+lambda_(1)hatj+3hatk,vec(b)=4hati+(3-lambda_(2))hatj+6hatk` and `vec( c )=3hati+6hatj+(lambda_(3)-1)hatk` are three vectors. Vector `vec(b)=2vec(a)` and `vec(a)` is perpendicular to `vec(b)` then the possible value of `(lambda_(1),lambda_(2),lambda_(3))` is ..............

A

`((1)/(2),4,-2)`

B

`(-(1)/(2),4,0)`

C

`(1,3,1)`

D

(1, 5, 1)

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The correct Answer is:
B
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk,vec( c )=hati+hatj-2hatk...

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  2. vec(a)=hati+hatj+sqrt(2)hatk,vec(b)=b(1)hati+b(2)hatj+sqrt(2)hatk and ...

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  3. vec(a)=2hati+lambda(1)hatj+3hatk,vec(b)=4hati+(3-lambda(2))hatj+6hatk ...

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  4. squareABCD is a parallelogram vec(AB)=bar(q),vec(AD)=bar(p),angleBAC i...

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  5. The position vectors of A, B and C are 2hati-hatj+hatk,hati-3hatj-5hat...

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  6. A particle is acted upon constant forces vec(F)(1)=4hati+hatj-3hatk an...

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  7. Let vec(u),vec(v) and vec(w) be such that |vec(u)|=1,|vec(v)|=2,|vec(w...

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  8. The centroid of DeltaABC is G. The angle between vec(GB) and vec(GC) i...

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  9. The area of the parallelogram whose diagonals are hatj+hatk and hati+h...

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  10. The area of the parallelogram whose adjacent side is hati+hatk and hat...

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  11. If bar(x) and bar(y) are non zero, non collinear vector then the numbe...

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  12. If |bar(x).bar(y)|=cos alpha, then |bar(x)xx bar(y)| = …………….

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  13. If bar(a)=(2,0,1) and bar(b)=(1,1,1) then sin(bar(a)""(,)^(hat)bar(b))...

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  14. The unit vector perpendicular to both the vectors (3, -1, 0) and (-2, ...

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  15. The area of the parallelogram with diagonals hati+hatj and hatj+hatk i...

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  16. The angle between the vectors (2,-1,1) and (1,-1,2) is ……………

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  17. If |bar(x)|=7.|bar(y)|=sqrt(2),bar(x)xx bar(y)=(6,2,3) then |bar(x).ba...

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  18. The unit vector perpendicualr to both the vectors hati+2hatj-2hatk and...

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  19. A(-1, 2, 3), B(1, 1, 1) and C(2, -1, 3) are three points in the plane....

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  20. If |bar(a).bar(b)|=3 and |bar(a)xx bar(b)|=4 then the angle between ba...

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