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Find the angles between the following pa...

Find the angles between the following pairs of vectors:
(i) `vec(A) = hati + hatj +hatk` and `vec(B) =- 2hati - hatj - 2 hatk`.
(ii) `vec(A) =- 2hati +2hatj - hatk` and `vec(B) = 3hati + 6 hatj +2 hatk`
(iii) `vec(A) = 4 hati +6 hatj - 3 hatk` and `vec(B) =- 2hati - 5hatj +7 hatk`

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The correct Answer is:
`180^(@), 79^(@), 148.9^(@)`
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SL ARORA-VECTORS-Problems For Self Practice
  1. Find the value of m so that the vector 3 hati - 2hatj +hatk is perpend...

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  2. For what value of a are the vectors vec(A) = a hati - 2hatj +hatk and ...

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  3. Find the angles between the following pairs of vectors: (i) vec(A) =...

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  4. Calculate the values of (i) hatj. (2hati - 3hatj +hatk) and (ii) (2hat...

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  5. A force vec(F) = 4 hati + hatj + 3hatk newton acts on a particle and d...

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  6. Under a force of 10 hati - 3 hatj +6 hatk newton, a body of mass 5 kg ...

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  7. The sum and difference of two vectors vec(A) and vec(B) are vec(A) +ve...

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  8. A force vec(F) = 5hati + 4hatj newton displaces a body through vec(S) ...

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  9. If the resultant of the vectors 3 hati +4 hatj +5 hatk and 5 hati +3 h...

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  10. Show that the vectors a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk and ...

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  11. If vectors vec(A),vec(B) and vec(C) have magnitudes 8,15 and 17 units ...

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  12. If vec A =vec B- vec C, then determine the angle between vec A and ve...

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  13. For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B...

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  14. Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos the...

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  15. Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 ha...

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  16. If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk, th...

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  17. Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and ...

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  18. Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3...

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  19. Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj...

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  20. Find a vector of magnitude 18 which is perpendicular to both the vecto...

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