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Given three vectors U=2hat(i)+3hat(j)-6h...

Given three vectors `U=2hat(i)+3hat(j)-6hat(k), V=6hat(i)+2hat(j)+2hat(k) and W=3hat(i)-6hat(j)-2hat(k)` which of the following hold good for the vectors U, V and W ?

A

U, V and W are linearly dependent

B

`(UtimesV)timesW=0`

C

U, V and W form a triplet of mutually perpendicular vectors

D

`Utimes(VtimesW)=0`

Text Solution

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The correct Answer is:
B, C, D
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
  1. Given the following informations about the non-zero vectors A, B and C...

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  2. Let a, b and c are non-zero vectors such that they are not orthogonal ...

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  3. Given three vectors U=2hat(i)+3hat(j)-6hat(k), V=6hat(i)+2hat(j)+2hat(...

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  4. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  5. Three vectors veca,vecb,vecc are such that vecaxxvecb= 3(vecaxxvecc)Al...

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  6. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

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  7. If veca and vecb are two unit vectors perpendicular to each other and...

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  8. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

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  9. If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j), then the vectors (a*hat...

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  10. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat ka n d...

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  11. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

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  12. Let the unit vectors a and b be perpendicular and the unit vector c be...

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  13. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

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  14. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

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  15. If veca and vecb are any two unit vectors, then find the greatest post...

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  16. If vec a is perpendicular to vec b and vec r is non-zero vector suc...

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  17. In a four-dimensional space where unit vectors along the axes are ...

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  18. A vector(d) is equally inclined to three vectors a=hat(i)-hat(j)+hat(k...

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  19. If a, b, c are non-zero, non-collinear vectors such that a vectors suc...

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  20. Given three vectors veca, vecb and vecc are non-zero and non-coplanar ...

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