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For any two vectors vec a and vec b, pro...

For any two vectors `vec a` and `vec b`, prove that `(vec a* vec b)^ 2 le |quad vec a|^2|quad vec b|^2`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Consider the points P (- 1, 0 2) and Q (3, -2 1), Write down vector v...

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  2. If vec a = 2hat i - hat j+ 3hat k and vec b =4 hat i+ hat j - 3 hat k,...

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  3. For any two vectors vec a and vec b, prove that (vec a* vec b)^ 2 le |...

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  4. If for a vector vec a, vec a*hat i = vec a*hat j= vec a*hat k=0, then ...

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  5. If |vec a|=10, and |vec b|=2 and vec a* vec b =12, find angle between ...

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  6. What is the area of a triangle, two of whose sides are along the vecto...

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  7. If vec a and vec b are the position vectors of A and B respectively, f...

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  8. Evaluate int sin2x dx/(1-sinx)

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  9. Find the sine of the angle between the vectors vec a =3 hat i+hat j+2 ...

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  10. Find a vector of magnitude 6 units which is at right angles to both th...

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  11. A vector vec(r ) is inclined at equal angles to the three axes. If the...

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  12. If vec a = 6hat i - hat j+ 2hat k and vec b =hat i- 3hat j - 2 hat k, ...

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  13. What is the value of [vec a vec b vec c] if vec a, vec b, vec c are no...

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  14. If a and b are two unit vectors such that a+2b and 5a−4b are perpendic...

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  15. If vec a = 7 hat i +hat j - 4 hat kand vec b=2 hat i+6 hat j +3 hat k,...

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  16. What is the value of |hat a+ hat b + hat c| if hat a, hat b and hat c ...

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  17. If vec a=4 hat i -hat j +hat k and vec b =2hat i-2 hat j+hat k, then f...

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  18. Find λ and μ if (hat i+3 hat j+9 hat k) xx (3 hat i-λ hat j+μ hat k) =...

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  19. If vec a = 2hat i -3 hat j+ 3hat k and vec b =3 hat i- hat j - 4 hat k...

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  20. Classify the following measures as scalars and vectors, 10 g

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