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

`bar(d)=lambda(bar(a)xx bar(b))+mu(bar(b)xx bar( c ))+v(bar( c )xx bar(a))` and `[bar(a)bar(b)bar( c )]=(1)/(8)` then `lambda+mu+v` = …………..

A

`bar(d)*(bar(a)+bar(b)+bar( c ))`

B

`2bar(d).(bar(a)+bar(b)+bar( c ))`

C

`4bar(d).(bar(a)+bar(b)+bar( c ))`

D

`8bar(d)*(bar(a)+bar(b)+bar( c ))`

Text Solution

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The correct Answer is:
D
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If (bar(a)xx bar(b))xx(bar(b)xx bar( c ))=bar(b) , where bar(a),bar(b),bar( c ) are non zero vectors, then …………..

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

For three vectors bar(a),bar(b) and bar( c ),bar(a)xx(bar(b)xx bar( c ))=(bar(a)xx bar(b))xx bar( c ) then

If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar(a)xx(bar(b)xx(bar( c )xx bar(d))))=K[bar(a),bar( c ),bar(d)] then K = ….

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

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

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  4. The volume of the tetrahedron whose vertices hati-6hatj+10hatk,-hati-3...

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  5. bar(a),bar(b) and bar( c ) are three non zero, non planar vectors. bar...

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  6. bar(a)=(1,2,-3),bar(b)=(2,1,-1). The vector bar(mu) is such that bar(a...

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  7. bar(a)=a(1)hati+a(2)hatj+a(3)hatk,bar(b)=b(1)hati+b(2)hatj+b(3)hatk,ba...

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  8. The adjacent sides of the parallelogram are bar(a)=3bar(alpha)-bar(bet...

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  9. bar(alpha)=2hati+3hatj-hatk,bar(beta)=-hati+2hatj-4hatk and bar(gamma)...

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  10. If bar(mu)=hati xx(bar(a)xx hati)+hatj xx(bar(a)xx hatj))+hatk xx(bar(...

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  11. bar(a),bar(b) and bar( c ) are three unit vectors. bar(a)|bar(b) and b...

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  12. bar(a)=2hati+hatj-2hatk and bar(b)=hati+hatj. The vector bar( c ) is s...

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  13. The vectors bar(a) and bar(b) are perpendicular then bar(a)xx{bar(a)xx...

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  14. If bar(a),bar(b),bar( c ) and bar(d) are coplanar vectors then (bar(a)...

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  15. bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

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  16. For three vectors bar(a),bar(b) and bar( c ),bar(a)xx(bar(b)xx bar( c ...

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  17. If bar(a)=hati+hatj+hatk,bar(b)=hati+hatj,bar( c )=hati and (bar(a)xx ...

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  18. [bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

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  19. If (bar(a)xx bar(b))xx(bar(b)xx bar( c ))=bar(b), where bar(a),bar(b),...

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  20. If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar...

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