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What is geometrical significance of the relation `|veca+vecb|` = `|veca-vecb|`

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|veca| = |vecb| = veca = vecb .

Prove that : |veca + vecb|le|veca|+|vecb| .

State when the equality will hold, |veca - vecb|ge|veca|-|vecb|

Find a unit vector perpendicular to both of the vectors veca + vecb and veca - vecb where veca = hati + hatj + hatk and b = hati+2hatj+3hatk .

If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb| .

Find the angle between veca and vecb if |vecaxxvecb| = veca.vecb

Prove that two vactors are perpendicular iff |veca+vecb|^2 = |veca|^2 + |vecb|^2

Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2 .

If veca=hati+2hatj-3hatkand vecb=3hati-hatj+2hatk ,then find the angle between veca+vecb and veca-vecb.

What is the angle between veca and vecb if abs(veca+vecb)=abs(veca-vecb) ?

ARIHANT PUBLICATION-VECTOR ALGEBRA -Odisha Bureau.s Textbook Solutions (Exericise 12(a))
  1. Prove that |a+b| le |a| + |b| State when equality will hold,

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  2. Prove that |a-b| ge |a| - |b|

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  3. What is geometrical significance of the relation |veca+vecb| = |veca-v...

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  4. Find the magnitude of the vector vec(PQ), its scalar components and th...

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  5. Find the magnitude of the vector vec(PQ), its scalar components and th...

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  6. Find the magnitude of the vector vec(PQ), its scalar components and th...

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  7. In each of the following find the vector vec(PQ), its magnitude and di...

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  8. In each of the following find the vector vec(PQ), its magnitude and di...

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  9. If a = (2, -2, 1), b = (2, 3, 6) and c = (-1, 0, 2) find the magnitude...

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  10. Determine the unit vector having the direction of the given vector in ...

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  11. Determine the unit vector having the direction of the given vector in ...

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  12. Determine the unit vector having the direction of the given vector in ...

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  13. Determine the unit vector having the direction of the given vector in ...

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  14. Find the unit vector in the direction of the vector r(1) - r(2), where...

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  15. Find the unit vector parallel to the sum of the vectors veca = 2hati+4...

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  16. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  17. The position vectors of the points A, B, C and D are 4hati+3hatj-hatk,...

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  18. In each of the following problems, show by vector method that the give...

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  19. In each of the following problems, show by vector method that the give...

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  20. Prove that the vectors 2hat(i) - hat(j) + hat(k), hat(i) - 3hat(j) - 5...

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