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If `overline(a), overline(b), overline(c)` are unit vectors such that `overline(a)*overline(b)=(1)/(2), overline(b)*overline(c)=(1)/(sqrt(2)` and `overline(c)*overline(a)=(sqrt(3))/(2)`, then `overline(a)*(overline(b)timesoverline(c))=`

A

`(sqrt(sqrt(6)-2))/(2)`

B

`(sqrt(sqrt(6)+2))/(2)`

C

`(sqrt(6)-2)/(2)`

D

`(sqrt(6)+2)/(2)`

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The correct Answer is:
A
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NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. If overline(a)=hat(i)+2hat(k), overline(b)=2hat(i)+hat(j), overline(c)...

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  2. If overline(a)=2hat(i)+3hat(j)-hat(k), overline(b)=5hat(i)-6hat(j)+2ha...

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  3. If overline(a), overline(b), overline(c) are unit vectors such that ov...

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  4. If overline(a)=hat(i)+hat(j)+hat(k), overline(b)=2hat(i)+qhat(j)+hat(k...

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  5. If overline(a)=hat(i)+hat(j)+hat(k), overline(b)=2hat(i)+lambdahat(j)+...

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  6. If the vectors overline(a)=hat(i)+hat(j)+hat(k), overline(b)=hat(i)-h...

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  7. If the vectors overline(a)=hat(i)-hat(j)-6hat(k), overline(b)=hat(i)+...

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  8. If the vectors overline(a)=-3hat(i)+4hat(j)-2hat(k), overline(b)=hat(...

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  9. If the vectors overline(a)=4hat(i)+13hat(j)-18hat(k), overline(b)=hat...

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  10. If the vectors overline(a)=hat(i)-2hat(j)+hat(k), overline(b)=2hat(i)...

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  11. If the vectors overline(a)=hat(i)-2hat(j)+hat(k), overline(b)=phat(i)...

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  12. If the vectors overline(a)=hat(i)+hat(j)+hat(k), overline(b)=hat(i)-h...

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  13. If the vectors overline(a)=4hat(i)+11hat(j)+mhat(k), overline(b)=7hat...

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  14. If overline(a)=hat(i)-2hat(j)+hat(k), overline(b)=xhat(i)-5hat(j)+3hat...

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  15. Let overline(a)=hat(i)-hat(k), overline(b)=xhat(i)+hat(j)+(1-x)hat(k),...

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  16. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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  17. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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  18. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahati...

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  19. If overline(a)=hat(i)+hat(j), overline(b)=hat(j)+hat(k), overline(c)=a...

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  20. Let a,b,c be distinct non- negative numbers . If the vectors ah...

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