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P and Q are two points with position ...

`P` and `Q` are two points with position vectors `3 vec a-2 vec b` and ` vec a+ vec b` respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

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The correct Answer is:
`-vec(a)+4vec(b)`
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MODERN PUBLICATION-VECTOR ALGEBRA -EXERCISE 10 (c ) Short Answer Type Questions
  1. For given vectors, -> a=2 hat i- hat j+2 hat kand -> b=- hat i+ hat...

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  2. A and B are two points with position vectors 2vec(a)-3vec(b) and 6vec(...

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  3. P and Q are two points with position vectors 3 vec a-2 vec b and v...

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  4. X and Y are two points with position vectors 3vec(a)+vec(b) and vec(a)...

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  5. Find the position vector of the mid-point of the vector joining point ...

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  6. Find the position vector of the mid point of the ne segment A B ,\ wh...

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  7. Find a vector in the direction of the vector 5 hat i - hat j + 2 h...

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  8. Find a vector in the direction of vec a=2 hat i- hat j+2 hat k , whic...

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  9. Find a vector in the direction of : vec(a)=hat(i)-2hat(j)+2hat(k),...

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  10. Find a vector in the direction of : vec(a)=-2hat(i)+hat(j)+2hat(k)...

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

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  12. If |vec(a)|=3, what is : |5vec(a)|

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  13. If |vec(a)|=3, what is : |-2vec(a)|

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  14. If |vec(a)|=3, what is : |0vec(a)| ?

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  15. If vec(a)=3hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)-4 hat(j)-3 hat(k), fi...

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  16. Let vec(a) be a given vector whose initial point is P(x(1), y(1)) and ...

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  17. In the following, find the components of the vector vec(PQ) along x an...

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  18. If the position vectors of the points A and B are : 7hat(i)+3hat(j)-ha...

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  19. Find the position vector of the centroid of the Delta ABC when the pos...

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  20. Show that the vectors vec(a)=2hat(i)+3hat(j) and vec(b)=4hat(i)+6hat(...

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