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Find the position vector of a point R wh...

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `hati+2hatj-hatk` and `-hati+hatj+hatk` respectively, in the ratio 2 : 1.
(i) internally (ii) externally

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The correct Answer is:
(i) `R=-(1)/(3)hati+(4)/(3)hatj+(1)/(3)hatk`
(ii) `=-3hati+3hatk`
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KUMAR PRAKASHAN-VECTOR ALGEBRA -EXERCISE-10.2
  1. Compute the magnitude of the following vectors : veca=hati+hatj+k,...

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  2. Compute the magnitude of the following vectors : veca=hati+hatj+k,...

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  3. Write two different vectors having same magnitude.

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  4. Write two different vectors having same direction.

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  5. Find the values of x and y so that the vectors 2hati+3hatjandxhati+yh...

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  6. Find the scalar and vector components of the vector with initial poi...

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  7. Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5h...

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  8. Find the unit vector in the direction of the vector veca=hati+hatj+2h...

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  9. Find the unit vector in the direction of vector vec(PQ) , where P and ...

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  10. For given vectors veca=2hati-hatj+2hatkandvecb=-hati+hatj-hatk, find t...

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  11. Find a vector in the direction of vector 5hati-hatj+2hatk which has ma...

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  12. Show that the vectors 2hati-3hatj+4hatkand-4hati+6hatj-8hatk are coll...

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  13. Find the direction cosines of the vector hati+2hatj+3hatk.

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  14. Find the direction cosines of the vector joining the points A(1,2,-3)...

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  15. Show that the vector hati+hatj+hatk is equally inclined to the axes OX...

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  16. Find the position vector of a point R which divides the line joining t...

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  17. Find the position vector of the mid point of the vector joining the p...

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  18. Show that the points A, B and C with position vectors, vec(a)=3hati-4h...

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  19. If triangle ABC (Fig 10.18), which of the following is not true : (A...

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  20. If vec(a) and vec(b), are two collinear vectors, then which of the fol...

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