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Prove that |veca|-|vecb| le|veca - vecb ...

Prove that `|veca|-|vecb| le|veca - vecb |`.

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For any two vectors veca and vecb , prove that : |veca+vecb|le|veca|+|vecb| . Also, write the name of this inequality

For any two vectors vecaandvecb , prove that |veca+vecb|le|veca|+|vecb| . Also write the name of this inequality.

For any two vectors veca and vecb , prove that |veca.vecb|le|veca||vecb| Also write the name of this inequality.

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

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 .

Find |veca-vecb| , if two vectors veca and vecb are such that |veca|=2,|vecb|=3 and veca*vecb=4 .

State whether it is true or false If veca, vecb are two vectors then |veca.vecb|le|veca||vecb|

Prove that veca*((vecb+vecc)xx(veca+vecb+vecc))=0 .

MODERN PUBLICATION-VECTORS-Exercise
  1. If ABCDEF is a regular hexagon and AB+AC+AD+AE+AF=lamdaAD, then lamda ...

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  2. ABCDEF is a regular hexagon. Show that : vec(AB)+vec(AC)+vec(AD)+vec(A...

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  3. Prove that |veca|-|vecb| le|veca - vecb |.

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  4. If veca+5vecb=vecc and veca -7 vecb =2vecc, then show that veca has th...

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  5. Write two different vectors having same magnitude.

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  6. Write two different vectors having same direction.

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  7. Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5ha...

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  8. Find the vector with initial point P(-4,2) and terminal point Q(0,-4).

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  9. Find a unit vector in the direction from : P(3,2) towards Q(5,6).

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  10. Find a unit vector in the direction from : P(1,2) towards Q(4,5).

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  11. Compute the magnitude of the following vectors: vecc=(1/sqrt3)veci+(1/...

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  12. Find the magnitude of the vector hati-3hatj+4hatk.

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  13. Find the value of x for which x(hati + hatj + hatk) is a unit vector.

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  14. Find the unit vector in the direction of the vector veca=hati+hatj+2ha...

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  15. Find the unit vector in the direction of the vector : veca =2hati+3hat...

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  16. Find the unit vector in the direction of the vector : veca =3hati+2hat...

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  17. Find the unit vector in the direction of the vector : vecb =2hati+hatj...

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  18. Find the unit vector in the direction of the vector : veca =2hati-3hat...

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  19. Find the unit vector in the direction of vector vec(PQ, where P and Q ...

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  20. Find the values of x and y so that the vectors 2veci+3vecj and xveci+y...

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