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If a, b and c be the three non-zero vect...

If a, b and c be the three non-zero vectors satisfying the condition `atimesb=c and btimesc=a`, then which of the following always hold(s) good?

A

a, b and c are orthogonal in pairs

B

[a b c]=|b|

C

[a b c]`=|c^(2)|`

D

`|b|=|c|`

Text Solution

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The correct Answer is:
A, C
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
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  2. If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n ...

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  3. If a, b and c be the three non-zero vectors satisfying the condition a...

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  4. Given the following informations about the non-zero vectors A, B and C...

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

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

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

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

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

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

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

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  13. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and v...

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

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  15. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  16. If a, b, c are three non-zero vectors, then which of the following sta...

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

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

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  19. If a is perpendicular to b and p is non-zero scalar such that pr+(r*b)...

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

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