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प्रश्न
Find the position vector of point R which divides the line joining the points P and Q whose position vectors are `2hati - hatj + 3hatk` and `- 5hati + 2hatj - 5hatk` in the ratio 3:2 is internally.
उत्तर
It is given that the points P and Q have position vectors `barp = 2hati - hatj + 3hatk` and `barq = - 5hati + 2hatj - 5hatk` respectively.
If R(`barr`) divides the line segment PQ internally in the ratio 3:2, by section formula for internal division,
`barr = (3q + 2p)/(3 + 2)`
= `(3 (- 5hati + 2hatj - 5hatk) + 2(2hati - hatj + 3hatk))/5`
= `(- 11hati + 4hatj - 9hatk)/5`
= `1/5(- 11hati + 4hatj - 9hatk)`
∴ Coordinates of R = `(- 11/5, 4/5, -9/5)`
Hence, the position vector of R is `1/5(- 11hati + 4hatj - 9hatk)` and the coordinates of R are `(- 11/5, 4/5, -9/5)`
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