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If vec(a) = 5 hat(i) - hat(j) - 3 hat(k)...

If `vec(a) = 5 hat(i) - hat(j) - 3 hat(k)` and `vec(b) = hat(i) + 3 hat(j) - 5 hat(k)` , find the angle between `vec(a)` and `vec(b)`.

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`veca.vecb=5-3+15=17`
`|veca|=sqrt((5)^(2)+(-1)^(2)+(-3)^(2))=sqrt(35)`
`|vecb|=sqrt(1^(2)+(3)^(2)+(-5)^(2))=sqrt(35)`
`costheta=(veca.vecb)/(|veca||vecb|)=(17)/(35)`
`theta=cos^(-1)((17)/(35))`
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CP SINGH-VECTORS-Excercises
  1. If vec(a) = 5 hat(i) - hat(j) - 3 hat(k) and vec(b) = hat(i) + 3 hat(j...

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  2. A vector is not changed if

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  3. Two forces, each of magnitude F have a resultant of the same magnitude...

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  4. Two vectors acting through a point are in the ratio 3 : 5. If the angl...

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  5. The magnitude of vectros vec A, vec B and vec C are 12, 5 and 13 units...

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  6. If vec(A)=vec(B)+vec(C ), and the magnitudes of vec(A),vec(B),vec(C ) ...

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  7. Two forces, while acting on particle in opposite directions,have the r...

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  8. One of the following forces is double and the other resultant is equal...

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  9. Two vectors of magnitude 4 and 6 are acting through a point. If the ma...

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  10. The resultant of vecA and vecB makes an angle alpha with vecA and beta...

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  11. Which of the sets given below may represent the magnitudes of three ve...

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  12. The following sets of three vectors act on a body, whose resultant ...

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  13. Three vectors vec(P) , vec(Q) and vec( R) are such that |vec(P)| , |ve...

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  14. Three forces 9 , 12 and 15 N acting at a point are in equilibrium . T...

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  15. If the resultant of n forces of different magnitudes acting at a point...

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  16. Let vec(C )= vec(A)+vec(B) then

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  17. Forces of 1 and 2 units act along the lines x = 0 and y = 0. The equ...

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  18. The sum of two forces at a point is 16N. if their resultant is normal...

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  19. A particle is being acted upon by four forces of 30 N due east , 20 N ...

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  20. Six vector vec(a) through vec(f) have the magnitudes and direction ind...

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  21. If N-vectors of equal magnitude are acting through a point and angle b...

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