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If theta is the angle between the unti ...

If `theta` is the angle between the unti vectors `vec a` and `vec b` , then proves that `cos((theta)/(2)) = 1/2 |vec a + vec b|`.

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NEW JOYTHI PUBLICATION-VECTOR ALGEBRA-ADDITIONAL QUESTIONS FOR PRACTICE 10.3
  1. Find vec a. vec b, when vec a = hat i + hat j + 2 hat k and vec b = 3 ...

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  2. Find the angle between the vectors veca and vecb such that |vec a| = |...

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  3. Find veca. vec b when veca = 2 hat i + 2 hat j - hat k and vec b = 6 h...

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  4. Find lambda if the vectors 5 hat i + 2 hat j - hat k and lambda hat i ...

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  5. If vec a = 5 hat i - hat j - 3 hat k and vec b = hat i + 3 hat j - 5 ...

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  6. Consider the vectors veca = hat i + 3 hat j + hat k and vec b = 2 hat ...

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  7. Prove that the vectors 3 hat i + hat j + 3 hat k and hat i - hat k are...

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  8. If A(0,1,1), B(3, 1,5) and C(0, 3, 3) are three points show that Delta...

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  9. If vec a is a unit vector and (vec x - vec a).(vec x + vec a) = 8, the...

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  10. Find the angle betweeen two vectors vec a and vec b with magnitudes 2 ...

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  11. Find |vec a| and |vec b| if (vec a + vec b).(vec a - vec b) = 3 and 2|...

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  12. Find |vec a - vec b|, if |vec a| = 4, vec b = 12 and vec a. vecb = 16.

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  13. Find the magnitude of two vectors veca and vec b having the same magni...

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  14. If theta is the angle between the unti vectors vec a and vec b , then...

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  15. If vec a and vec b are two non- zero vectors such that | vec a + vec b...

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  16. If vec a and vec b are two vectors such that vec a + vec b is perpen...

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  17. If vec a and vec b are orthogonal vectors, prove that (vec a + vec b...

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  18. Consider the vectors vec a = hat i + 2 hat j - 3 hat k and vec b = 4 h...

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  19. If vec a + vec b + vec c=0 and |vec a|=3, |vec b|=5, |vec c| =7, show ...

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  20. (i) Write the scalar componets of 3 hat i - 2 hat j + 5 hat k. (ii) F...

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