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P and Q are two points with position vectors `2veca+2vecb` and `veca +vecb` 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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P and Q are two points with position vectors 3veca-3vecb and veca+vecb 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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Consider two points P and Q with position vectors vec(OP) = 3veca-2vecb and vec(OQ) = veca + vecb . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, externally.

Consider two points P and Q with position vectors vec(OP) = 3veca-2vecb and vec(OQ) = veca + vecb . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, internally.

If A and B are two points whose position vectors are 3hati+2hatj-2hatk and hati-3hatj-hatk respectively. Find the position vectors of the points dividing the segment AB externally in the ratio 3:1.

If A and B are two points whose position vectors are 3hati+2hatj-2hatk and hati-3hatj-hatk respectively. Find the position vectors of the points dividing the segment AB internally in the ratio 1:3.

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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 P(2veca + vecb) and Q(veca-3vecb) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

MODERN PUBLICATION-VECTORS-Exercise
  1. For given vectors,veca=2hati-hatj+2hatk and vecb=-hati+hatj-hatk , fin...

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  2. A and B are two points with position vectors 2veca-3vecb and 6vecb-vec...

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  3. P and Q are two points with position vectors 2veca+2vecb and veca +vec...

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  4. Consider two points P and Q with position vectors vec(OP) = 3veca-2vec...

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

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  6. Find the position vector of mid point of the line segment AB where A i...

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  7. Find a vector in the direction of : veca=3hati-hatj+2hatk, which has m...

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  8. Find a vector in the direction of : hati-2hatj+2hatk, which has magnit...

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  9. Find a vector in the direction of : -2hati+hatj+2hatk, which has magni...

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  10. Find the scalar components and magnitude of the vector joining the poi...

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  11. If |veca|=3, what is |5veca|.

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  12. If |veca|=3, what is : |-2veca|.

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  13. If |veca|=3, what is : |0veca|?

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  14. If veca =3hati-2hatj+hatk,vecb=2hati-4hatj-3hatk, find |veca-2vecb|.

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  15. Let a. =hati+2hatj and vecb =2hati+hatj. Is |veca |=|vecb |? Are the v...

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  16. Find the vector with initial point P(-4,2) and terminal point Q(0,-4).

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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 point A and B are : 7hati+3hatj-hatk an...

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  19. Find the position vector of the centroid of the /\ABC when the positio...

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  20. Show that the vectors veca=2hati+3hatj and vecb=4hati+6hatj are parall...

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