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For any vector vec(a),(vec(a)xx vec(i))^...

For any vector `vec(a),(vec(a)xx vec(i))^(2)+(vec(a)xx hatj)^(2)+(vec(a)xx vec(k))^(2)`= ……….. .

A

`4a^(2)`

B

`2a^(2)`

C

`a^(2)`

D

`3a^(2)`

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The correct Answer is:
B
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vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk . The vector vec(b) is such that vec(a) xx vec(b)+vec( c )=0 and vec(a)*vec(b)=3 then vec(b) = ………..

KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. The vectors vec(a) and vec(b) are not perpendicular. The vectors vec( ...

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  2. vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk. The vector vec(b) is suc...

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  3. For any vector vec(a),(vec(a)xx vec(i))^(2)+(vec(a)xx hatj)^(2)+(vec(a...

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  4. vec(a),vec(b) and vec( c ) are three vector vec(a)ne0 and |vec(a)|=|ve...

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  5. For any vecotr vec(a), The value of hati xx(vec(a)xx hati)+j xx(vec(a)...

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  6. If (a(1),1,1),(1,a(2),1) and (1,1,a(3)) are coplaner (where a(i)ge1,i=...

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  7. If bar(x)=(1,-1,0),bar(y)=(0,1,3) and bar(z)=(2,1,1) then bar(x)xx (ba...

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  8. If [vec(a)xx vec(b),vec(b)xx vec( c ),vec( c )xx vec(a)]=lambda[vec(a)...

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  9. The volume of a parallelepiped with edges vec(OA)=(3,1.4),vec(OB)=(1,2...

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  10. Let vec(a),vec(b) and vec( c ) are three unit vectors such that vec(a)...

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  11. If |bar(a)|=1 and bar(a)xx bar(b)=(1,2,3) then bar(a)xx[bar(a)xx(bar(a...

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  12. If bar(x)xx(bar(y)xx bar(z))=(bar(x)xx bar(y))xx bar(z) then bar(y)xx(...

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  13. Let vec(a)=2hati+hatj-2hatk and vec(b)=hati+hatj. Let the vector vec( ...

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  14. If the unit bar(a),bar(b) and bar( c ) are coplanar then …………..

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  15. If bar(a),bar(b) and bar( c ) are not coplanar then (bar(a)+bar(b)+b...

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  16. If the vectors 3hati-2hatj-hatk,2hati-3hatj-4hatk,-hati+hatj+2hatk and...

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  17. If the unit vectors bar(a),bar(b) and bar( c ) are coplanar then [2ba...

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  18. vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk,vec( c )=hati+hatj-2hatk...

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  19. bar(a),bar(b) and bar( c ) are non zero vectors. |(bar(a)xx bar(b))*...

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  20. bar(d)=lambda(bar(a)xx bar(b))+mu(bar(b)xx bar( c ))+v(bar( c )xx bar(...

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