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Vector Algebra

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  1. 351.Let a, b and c be non-zero vectors such that a( b c)=13| b|| c| a.
  2. 352.If t_1 and t_2 are the times of flight of two particles having the same initial velocity u…
  3. 353.A velocity of 14 m/s is resolved into two components along OA and OB making angles 30^ and…
  4. 354.A particle moves towards east from a point A to a point B at the rate of 4 km/h and then t…
  5. 355.Three forces P, Q and R acting along IA, IB and IC, where I is the incentre of a ABC, are …
  6. 356.In a right angle ABC, A=90^ and sides a,b,c are respectively 5 cm, 4 cm and 3 cm.
  7. 357.With two forces acting at a point, the maximum effect is obtained when their resultant is …
  8. 358.A particle is acted upon by constant forces 4 i+ j-3 k and 3 i+ j- k which displace it fro…
  9. 359.Consider points A,B,C and D with position vectors 7 i-4 j+7 k, i-6 j+10 k, - i-3 j+4 k and…
  10. 360.If vmatrixa&a^2&1+a^3&b^2&1+b^3&c^2&1+c^3vmatrix=0 and the vectors (1,a,a^2), (1,b,b^2) an…
  11. 361.a, b, c are 3 vectors such that a+ b+ c= 0, | a|=1, | b|=2, | c|=3, then a b+ b c+ c a is …
  12. 362.If u, v and w are three non-coplanar vectors, then ( u+ v- w)[( u- v)( v- w)] equals:
  13. 363.A tetrahedron has vertices at O(0,0,0), A(1,2,1), B(2,1,3) and C(-1,1,2).
  14. 364.Let u= i+ j, v= i- j and w= i+2 j+3 k.
  15. 365.Two particles start simultaneously from the same point and move along two straight lines, …
  16. 366.Two stones are projected from the top of a cliff h metres high, with the same speed u, so …
  17. 367.A body travels a distance s in t seconds.
  18. 368.The resultant of forces P and Q is R.
  19. 369.A couple is of moment G and the force forming the couple is P.
  20. 370.A particle acted on by constant forces 4 i+ j-3 k and 3 i+ j- k is displaced from the poin…
  21. 371.If | a|=5, | b|=4, | c|=3, what will be the value of a b+ b c+ c a, given that a+ b+ c= 0?
  22. 372.If a, b, c are vectors such that a+ b+ c= 0 and | a|=7, | b|=5, | c|=3, then the angle bet…
  23. 373.If a b= b c= c a, then a+ b+ c=
  24. 374.a=3 i-5 j and b=6 i+3 j are two vectors, and c is a vector such that c= a b, then | a|:| b…
  25. 375.If the vectors c, a=x i+y j+z k and b= j are such that a, c, b form a right handed system,…
  26. 376.If a, b, c are vectors such that [ a b c]=4, then [( a b) ( b c) ( c a)]=
  27. 377.If | a|=4, | b|=2 and the angle between a and b is /6, then | a b|^2 is equal to:
  28. 378.A bead of weight w can slide on a smooth circular wire in a vertical plane.
  29. 379.The sum of two forces is 18 N and the resultant, whose direction is at right angles to the…