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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

MODERN PUBLICATION-VECTOR-EXERCISE
  1. Determine the area of parallelogram whose adjacent sides are the vecto...

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  2. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  3. Prove that (vec a × vec b).(vec c × vec d) = [[vec a.vec c,vec a.vec d...

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  4. Find a unit vector in direction of vec a-vec b, when vec a = 4 hat i +...

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  5. If vec a and vec b be perpendicular vectors, then prove that (vec a + ...

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  6. Find the value of lambda so that the three vectors are co-planar. (2,-...

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  7. Determine k such that a vector vec(r) is at right angles to each of th...

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  8. Find the scalar and vector projection of veca on vecb. veca = hati+hat...

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

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

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  11. Show that vec a × (vec b+vec c) + vec b × (vec c+vec a) + vec c × (vec...

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  12. If vec(a) and vec(b) are unit vectors, then what is the angle between ...

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  13. Prove by vector method that the diagonals of a parallelogram bisect ea...

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  14. Prove by vector method that in a parallelogram, the line joining a ve...

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

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  16. Prove the following by vector method. Median to the base of an isoscel...

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  17. Prove the following by vector method. The diagonals of a rhombus are a...

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  18. Prove the following by vector method. An angle inscribed in a semi-cir...

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  19. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  20. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

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