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If |vecaxxvecb|=2,|veca.vecb|=2, then |v...

If `|vecaxxvecb|=2,|veca.vecb|=2`, then `|veca|^(2)|vecb|^(2)` is equal to

A

6

B

2

C

8

D

20

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If veca and vecb are any two vectors , then prove that |vecaxxvecb|^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2)=|{:(veca.veca,veca.vecb),(veca.vecb,vecb.vecb):}| or |vecaxxvecb|^(2)+(veca.vecb)^(2)=|veca|^(2)|vecb|^(2) (This is also known as Lagrange identily)

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AAKASH INSTITUTE-VECTOR ALGEBRA-ASSIGNMENT (SECTION-A)
  1. hati.(hatjxxhatk)+hatj.(hatixxhatk)+hatk.(hatixxhatj) is equal to

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  2. For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxx...

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  3. If |vecaxxvecb|=2,|veca.vecb|=2, then |veca|^(2)|vecb|^(2) is equal to

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  4. |(vecaxxvecb)|^(2) is eqaul to

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  5. If veca and vecb are unit vectors, then which of the following values ...

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  6. If veca.veci=veca.(hati+hatj)=veca.(hati+hatj+hatk) . Then find the un...

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  7. If veca +vecb +vecc =vec0, |veca| =3 , |vecb|=5 and |vecc| =7 , then ...

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  8. The vector cosalpha.cosbetahati+cosalpha.sinbetahatj+sinalphahatk is a...

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  9. If |veca|=|vecb|, then (veca+vecb).(veca-vecb) is equal to

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  10. If veca and vecb are unit vectors inclined at an angle theta, then the...

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  11. The projection of the vector hati+hatj+hatk along the vector of hatj i...

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  12. If OACB is a parallelogram with vecOC=veca and vecAB=vecb, then vecOA ...

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  13. If veca, vecb, vecc, vecd are the position vectors of points A, B, C a...

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  14. If the vectors 3hati+lambdahatj+hatk and 2hati-hatj+8hatk are perpendi...

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  15. The vectors 2hati+hatj-4hatk and ahati+bhatj+chatk are perpendicular, ...

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  16. Let veca , vecb , vecc be three unit vectors such that |veca + vecb +...

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  17. If theta is the angle between the vectors 2hati-2hatj+4hatk and 3hati+...

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  18. If veca=2hati-3hatj-hatk and vecb=hati+4hatj-2hatk, then vecaxxvecb is

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  19. If veca,vecb represent the diagonals of a rhombus, then

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  20. If vecu=veca-vecb, vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvec...

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