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Prove that , ( vec(a) xx vec(b))^(2...

Prove that ,
` ( vec(a) xx vec(b))^(2) + (vec (a).vec(b))^(2) = |veca|^(2) |vec(b)|^(2)`

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A DAS GUPTA-Product of two Vectors-Exercise
  1. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

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  2. Prove that |vec a + vec b| = sqrt (|vec a|^2 + |vec b|^2 + 2 vec a * ...

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  3. Prove that , ( vec(a) xx vec(b))^(2) + (vec (a).vec(b))^(2) = |ve...

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  4. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then show that veca...

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  5. Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b...

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  6. If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a ...

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  7. Find lambda such that the scalar product of the vector vec i + vec j +...

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  8. The set of values of x for which the angle between the vectors vec a= ...

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  9. Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. ...

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  10. Vectors 3 vec a-5 vec ba n d2 vec a= vec b are mutually perpendicular....

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  11. The pth, qth and rth terms of a GP are the positive numbers a,b and c ...

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  12. If vec a, vec b , vec c are mutually perpendicular vectors of equal ma...

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  13. A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a...

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  14. vec a , vec b and vec c are the position vectors of points A ,B and C...

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  15. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

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  16. If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...

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  17. A , B , Ca n dD are any four points in the space, then prove that |...

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  18. If the angle between the vectors x vec i + vec j - vec k and vec i + x...

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  19. If the vector vec a= x vec i + y vec j + 2 vec k is perpendicular to t...

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  20. If vec a is a vector of magnitude 50 and parallel to vec b= 6 vec i - ...

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