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If overline(a)=hat(i)-hat(j), overline(b...

If `overline(a)=hat(i)-hat(j), overline(b)=hat(j)-hat(k), overline(c)=hat(k)-hat(i) and hat(d)` is a units vectors such that `overline(a)*hat(d)=[[overline(b), overline(c), overline(d)]]=0`, then `hat(d)=`

A

`(1)/(sqrt(2))|overline(a)||overline(b)|`

B

`(1)/(2)|overline(a)|^(2)|overline(b)|^(2)`

C

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

D

`pm(hat(i)+hat(j)-2hat(k))/(sqrt(6))`

Text Solution

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The correct Answer is:
D
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NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. If overline(a), overline(b) and overline(c) are non-coplanar and (over...

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  2. If overline(a), overline(b) and overline(c) are unit vectors perpendic...

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  3. The value of [[overline(a)-overline(b), overline(b)-overline(c), overl...

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  4. If |overline(a)|=5, |overline(b)|=3, |overline(c)|=4 and |overline(a)|...

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  5. If overline(a) is perpendicular to overline(b) and overline(c), |overl...

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  6. If |overline(c)|=1 and overline(c) is perpedicular to overline(a) and ...

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  7. If overline(a)=hat(i)-hat(j), overline(b)=hat(j)-hat(k), overline(c)=h...

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  8. If overline(b)=2hat(i)+hat(j)-hat(k), overline(c)=hat(i)+3hat(k) and o...

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  9. If overline(a), overline(b), overline(c) are linearly independent, the...

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  10. If overline(A),overline(B), overline(C) are three non-coplanar vector,...

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  11. If overline(a), overline(b), overline(c) are non-coplanar vectors and ...

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  12. If overline(a), overline(b), overline(c) are non-coplanar vectors and ...

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  13. If overline(b) and overline(c) are any two perpendicular unit vectors ...

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  14. If overline(a),overline(b), overline(c) are three non-coplanar vectors...

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  15. If overline(a),overline(b), overline(c) are three non-coplanar vectors...

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  16. If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(...

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  17. If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(...

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  18. If overline(a), overline(b), overline(c) are three non-coplanar vector...

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  19. If z1 and z2 are z co-ordinates of the point of trisection of the segm...

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  20. Let square PQRS be a quadrilateral. If M and N are the mid-points of t...

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