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Prove that (vec(A) +2vec(B)) .(2vec(A) -...

Prove that `(vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos theta - 6B^(2)`.

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SL ARORA-VECTORS-Problems For Self Practice
  1. If the resultant of the vectors 3 hati +4 hatj +5 hatk and 5 hati +3 h...

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  2. Show that the vectors a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk and ...

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  3. If vectors vec(A),vec(B) and vec(C) have magnitudes 8,15 and 17 units ...

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  4. If vec A =vec B- vec C, then determine the angle between vec A and ve...

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  5. For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B...

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  6. Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos the...

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  7. Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 ha...

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  8. If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk, th...

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  9. Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and ...

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  10. Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3...

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  11. Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj...

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  12. Find a vector of magnitude 18 which is perpendicular to both the vecto...

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  13. Determine the area of the parallelogram whose adjacent sides are forme...

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  14. Find the area of the triangle formed by points O,A and B such that vec...

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  15. Find with the help of vectors, the area of the triangle with vertices ...

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  16. If vec(A) and vec(B) are two such vectors that |vec(A)| = 2, |vec(B)| ...

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  17. Find the moment about the point hati + 2hatj - hatk of a force represe...

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  18. Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a...

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  19. Prove that |vec(a) xx vec(b)| = sqrt(a^(2)b^(2) -(vec(a) -vec(b))^(2))

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  20. If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2 hati - hatj - hatk and ve...

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