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

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

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

Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

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

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

Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

Vectors veca,vecb, vecc are such that veca + vecb + vecc = 0 and |veca| = 3, |vecb| = 5 and |vecc]= 7 . Find the angle between veca and vecb .

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

If veca,vecb and vecc are three vectors such that veca x vecb = vecc and vecb x vecc = veca , then prove that veca,vecb and vecc are mutually at right angles and |vecb| = 1,|vecc| = |veca|

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. If veca and vecb are unit vectors and veca+vecb is also a unit vector,...

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

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  3. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  4. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  5. Prove the following by vector method. Measure of the angle between two...

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  6. Prove by vector method that the lines joining the mid points of consec...

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  7. if veca=2hati-5hatj+8hatk, vecb=hati-3hatj-7hatk and vecc=-3hati+2hatj...

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  8. If veca = 3hati+3hatj+hatk and vecb = -2hati+hatj-2hatk then what is t...

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  9. Find the angle between the vectors 3hati + 4hatj and 2hati+hatj+sqrt3h...

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  10. What is the angle between two vectors veca and vecb with magnitude 2 a...

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  11. If veca = 3hati+3hatj+hatk and vecb = -2hati+hatj-2hatk then what is t...

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  12. Find the component of the vector vec(b) = 8hat(i) + hat(j) in the dire...

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  13. What is the value of x so that the vector 6hati+2hatj-3hatk and hati-4...

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  14. Determine mu, for which the vector vec(a)=mu(6hat(i)+2hat(j)-3hat(k)) ...

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  15. How many directions a null vector has ?

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  16. If veca,vecb andvecc are three mutually perpendicular vectors, each of...

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  17. What is the volume of the parallelopiped whose sides are given by the ...

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  18. Write the values of m and n for which the vectors (m-1)overset^i+(n+2)...

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  19. Show that the vectors 2hati + 3hatj,5hati -5hatk and 6hatj + 4hatk are...

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  20. If A, B, C, D, E are the.vertices of a regular pentagon, find the vect...

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