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Show that the altitude of /\ ABC through...

Show that the altitude of `/_\ ABC` through a vertex A is equal to `(|vec a xx vec b + vec b xx vec c + vec c xx vec a|)/(|vec b- vec c|)` where the position vectors of A,B, and C are respectively `vec a, vec b` and ` vec c`.

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A DAS GUPTA-Product of two Vectors-Exercise
  1. Show that the altitude of /\ ABC through a vertex A is equal to (|vec ...

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  2. For any vector vec r , prove that vec r=( vec rdot hat i) hat i+( ve...

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  3. If |vec(a)+vec(b)||=|vec(a)-vec(b)| then show that vec(a) and vec(b) a...

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  4. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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