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Find the position vector of a point `R` which divides the line joining two points `P` and `Q` whose position vectors are `(2\ vec a+ vec b)` and (` vec a-\ 3 vec b)` respectively, externally in the ratio 1:2.Also, show that `P` is the mid-point of the line segment `R Qdot`

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Find the position vector of a point R which divides the line joining the two points P and Q with position vectors vec OP=2vec a+vec b and vec OQ=vec a-2vec b, respectively in the ratio 1:2 internally and externally.

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MODERN PUBLICATION-VECTOR ALGEBRA -Miscellaneous Exercise on Chapter 10
  1. Write down a unit vector in XY-plane, making an angle of 30 with th...

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  2. Find the scalar components and magnitude of the vector joining the po...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

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  4. If vec(a)=vec(b)+vec(c ), then is it true that |vec(a)|=|vec(b)|+|vec(...

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  5. Find the value of x for which x( hat i+ hat j+ hat k)is a unit vector...

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  6. Find a vector of magnitude 5 units, and parallel to the resultant of ...

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  7. If -> a= hat i+ hat j+ hat k , -> b=2 hat i- hat j+3 hat k and -...

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  8. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

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  9. Find the position vector of a point R which divides the line joinin...

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  10. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  11. Show that the direction cosines of a vector equally inclined to the a...

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  12. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

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  13. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

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  14. If vec a , vec b , vec c are mutually perpenedicular vectors of eq...

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  15. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

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  16. If theta is the angle between two vectors vec a\ a n d\ vec b ,\ t h...

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  17. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

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  18. Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+ha...

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  19. If is the angle between any two vectors -> a and -> b , then ...

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