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If overline(a)*overline(b)=overline(b)*o...

If `overline(a)*overline(b)=overline(b)*overline(c)=overline(c)*overline(a)=0`, then `overline(a)*(overline(b)timesoverline(c))=`

A

a non-zero vector

B

`1`

C

`-1`

D

`|overline(a)||overline(b)||overline(c)|`

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The correct Answer is:
D
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[[overline(a), overline(b)+overline(c), overline(c)+overline(b)+overline(a)]]=

If overline(c)=3overline(a)-2overline(b) , then [[overline(a), overline(b), overline(c)]]=

|[overline(a)*overline(a), overline(a)*overline(b)], [overline(a)*overline(b), overline(b)*overline(b)]|=

If overline(a), overline(b), overline(c) are linearly independent, the ([[2overline(a)+overline(b), 2overline(b)+overline(c), 2overline(c)+overline(a)]])/([[overline(a), overline(b), overline(c)]])=

overline(a)*((overline(a)+overline(b)+overline(c))times(overline(b)+overline(c)))=

If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , where overline(a), overline(b), overline(c) are three non-coplanar vectors, then (overline(a)-overline(b)-overline(c))*overline(p)-(overline(b)-overline(c)-overline(a))*overline(q)-(overline(c)-overline(a)-overline(b))*overline(r)=

If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , where overline(a), overline(b), overline(c) are three non-coplanar vectors, then (overline(a)+overline(b)+overline(c))*(overline(p)+overline(q)+overline(r))=

NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. If hat(i), hat(j), hat(k) are the unit vectors and mutually perpendicu...

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  2. If overline(a), overline(b), overline(c) are three non-zero, non-copla...

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  3. If overline(a)*overline(b)=overline(b)*overline(c)=overline(c)*overlin...

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  4. For non-zero vectors overline(a), overline(b), overline(c), (overline(...

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  5. For non-zero vectors overline(a), overline(b), overline(c), (overline(...

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  6. If overline(x)*overline(a)=0, overline(x)*overline(b)=0, overline(x)*o...

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

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  8. If overline(a)=3hat(i)-2hat(j)+7hat(k), overline(b)=5hat(i)+hat(j)-2ha...

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  9. If overline(a)=3hat(i)-hat(j)+4hat(k), overline(b)=2hat(i)+3hat(j)-2ha...

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  10. If overline(a)=7hat(i)-hat(j)+2hat(k), overline(b)=hat(i)+3hat(j)-hat(...

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  11. If overline(a)=2hat(i)+3hat(j)-hat(k), overline(b)=4hat(i)+2hat(j)+3ha...

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  12. If overline(a)=hat(i)+2hat(k), overline(b)=2hat(i)+hat(j), overline(c)...

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

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

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

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

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

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

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

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

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