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If unit vectors hat(a) and hat(b) are in...

If unit vectors `hat(a)` and `hat(b)` are inclined at angle `theta`, then prove that
`|vec(a) - vec(b)| = 2 sin.(theta)/(2)`.

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SL ARORA-VECTORS-Example
  1. If hati and hatj are unit vectors along X-and Y-axis respective, then ...

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  2. Find the components of vec(a) = 2hati +3hatj along the direction of ve...

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  3. If unit vectors hat(a) and hat(b) are inclined at angle theta, then pr...

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  4. If vec(A) +vec(B) = vec(C) and A^(2) +B^(2) = C^(2), then prove that v...

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  5. Calculate the area of the parallelogram whose two adjacent sides are f...

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  6. If vec(A) and vec(B) denpte the sides of a parallelogram and its area ...

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  7. Determine a unit vecor perpendicular to both vec(A) = 2 hati +hatj +ha...

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  8. Find a vector whose length is 7 and which is perpendicular to each of ...

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  9. Determine the sine of the angle between the vectors 3 hati +hatj +2hat...

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  10. Show that (vec(A) - vec(B)) xx (vec(A) +vec(B)) = 2(vec(A) xx vec(B))

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  11. For any three vectors vec(A), vec(B) and vec(C) prove that vec(A) x...

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  12. For any to vectors vec A and vec B, prove that | vec A xx vec B|^2 ...

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  13. Find |vec(A) xx vec(B)| if |vec(A)| = 10|vec(B)| = 2 and vec(A).vec(B)...

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  14. Find vec(A).vec(B) if |vec(A)| = 2, |vec(B)| = 5 and |vec(A) xx vec(B)...

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  15. Find the area of the triangle formed by the tips of the vectors vec(a)...

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  16. Find the moment about the point (1,-1,-1) of the force 3 hati +4hatj -...

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  17. The diagonals of a parallelogram are gives by the vectors 3hati +hatj ...

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  18. Prove by the method of vectors that in a triangle a/(sin A)=b/(sinB)=c...

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  19. Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec...

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

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