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Find the position vector of point R which divides the line joining the points P and Q whose position vectors are ijk2i^-j^+3k^ and ijk-5i^+2j^-5k^ in the ratio 3 : 2 is internally. - Mathematics and Statistics

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Sum

Find the position vector of point R which divides the line joining the points P and Q whose position vectors are `2hat"i" - hat"j" + 3hat"k"`  and `- 5hat"i" + 2hat"j" - 5hat"k"` in the ratio 3 : 2 is internally.

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Solution

It is given that the points P and Q have position vectors `bar"p" = 2hat"i" - hat"j" + 3hat"k"` and `bar"q" = - 5hat"i" + 2hat"j" - 5hat"k"` respectively.

If R(`bar"r"`) divides the line segment PQ internally in the ratio 3 : 2, by section formula for internal division,

`bar"r" = (3bar"q" + 2bar"p")/(3 + 2)`

`= (3 (- 5hat"i" + 2hat"j" - 5hat"k") + 2(2hat"i" - hat"j" + 3hat"k"))/5`

`= (- 11hat"i" + 4hat"j" - 9hat"k")/5`

`= 1/5(- 11hat"i" + 4hat"j" - 9hat"k")`

∴ coordinates of R = `(- 11/5, 4/5, -9/5)`

Hence, the position vector of R is `1/5(- 11hat"i" + 4hat"j" - 9hat"k")` and the coordinates of R are `(- 11/5, 4/5, -9/5)`

Concept: Section Formula
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