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For any vector x, the value of (vecx×hat...

For any vector `x`, the value of `(vecx×hati)^2+(vecx×hatj)^2+(vecx×hatk)^2` is equal to

A

`2a^(2)`

B

`4a^(2)`

C

`3a^(2)`

D

`a^(2)`

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The correct Answer is:
A
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MCGROW HILL PUBLICATION-VECTOR ALGEBRA-QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
  1. Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)x...

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  2. If C is the mid-point of AB and P is any point outside AB, then

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  3. For any vector x, the value of (vecx×hati)^2+(vecx×hatj)^2+(vecx×hatk)...

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  4. Let a, b,c be distinct non-negative numbers. If the vectors ai + aj + ...

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  5. If bara,barb,barc are non-coplanar vectors and lambda is a real number...

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  6. Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c...

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  7. If (a xx b) xx c = a xx (b xx c). Where a,b and c are any three vector...

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  8. Values of a for which the points A, B, C with position vectors 2i - j+...

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  9. Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(...

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  10. If hat u and hat v are unit vectors and theta is the acute ang...

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  11. The vector veca=alpha hati+2hatj+betahatk lies in the plane of vectors...

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  12. The non-zero vectors are vec a,vec b and vec c are related by vec a= ...

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  13. If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...

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  14. vectors veca=i-j+2k , vecb=2i+4j+k and vecc=lambdai+j+muk are mutually...

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  15. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

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  16. If a=1/sqrt(10)(3i+k)" and "b=1/7(2i+3j-6k), then the value of (2a-b)....

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  17. The vectors a and b are not perpendicular and c and d are two vectors ...

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  18. If the vectors pi + j + k, i + qj + k and i + j + rk, where pneqnerne1...

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  19. Let a,b and c be three non-zero vectors which are pairwise non-colline...

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  20. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

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