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Prove that : (vecaxxvecb)^2=|\veca|^2.|\...

Prove that : `(vecaxxvecb)^2=|\veca|^2.|\vecb|^2-(veca.vecb)^2`.

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If veca and vecb are any two vectors, prove that (vecaxxvecb)^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2) It is known as Largange's indentity.

Prove that |vecaxxvecb|^2=|veca|^2|vecb|^2-(veca*vecb)^2=|:[veca*veca veca*vecb],[veca*vecb vecb*vecb]:| .

If veca" and "vecb are any two vectors, then (veca xx vecb)^(2)= |veca|^(2)|vecb|^(2)-(veca* vecb)^(2) .

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|

Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) .

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb)

Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2 , if and only if veca, vecb are perpendicular, given veca ne vec0, vecb ne vec0 .

If vecb and vecc are two non-collinear such that veca ||(vecbxxvecc) . Then prove that (vecaxxvecb).(vecaxxvecc) is equal to |veca|^(2)(vecb.vecc)

JMD PUBLICATION-VECTOR ALGEBRA-EXAMPLE
  1. Write the value of (hatixxhatj).k+(hatjxxhatk).hati.

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  2. Write the value of p for which veca=3hati+2hatj+9hatk and vecb=hati+ph...

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  3. Prove that : (vecaxxvecb)^2=|\veca|^2.|\vecb|^2-(veca.vecb)^2.

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  4. If veca=4hati+3hatj+hatk and vecb=hati-2hatk, find |\2vecbxxveca|.

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  5. The projection of veca=2hati-hatj+hatk on vecb=hati-2hatj+hatk is equa...

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  6. Find unit vector in the direction of veca+vecb, where veca=-hati+hatj+...

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  7. Find the angle between the vectors veca=hati-hatj+hatk and vecb=hati+h...

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  8. If |\veca|=sqrt3,|\vecb|=2 and angle between veca and vecb is 60^o. Fi...

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  9. If |\veca|=2,|\vecb|=sqrt3 and veca.vecb=sqrt3, find the angle between...

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  10. For what value of lambda are the vectors veca=2hati+lambdahatj+hatk an...

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  11. Find the projection of veca on vecb if veca.vecb=8 and vecb=2hati+6hat...

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  12. The value of : hati*(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) i...

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  13. Let veca and vecb be two vectors such that |\veca|=3 and |\vecb|=frac{...

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  14. What is the cosine of the angle which the vector sqrt(2hati)+hatj+hatk...

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  15. If vecp is a unit vector and (vecx-vecp).(vecx+vecp)=80, then find |\v...

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  16. Write a vector of magnitude 15 units in the direction of vector hati-2...

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  17. If veca and vecb are two vectors such that |\veca.vecb|=|\vecaxxvecb|,...

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  18. Find the angle between two vectors veca and vecb with magnitudes 1 and...

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  19. Find the value of p if (2hati+6hatj+27hatk)xx(hati+3hatj+phatk)=vec0...

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  20. For what value of 'a' the vectors 2hati-3hatj+4hatk and ahati+6hatj-8h...

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