# 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 externally. - Mathematics and Statistics

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 externally.

#### 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 joining P and Q externally in the ratio 3 : 2, by section formula for external division,

bar"r" = (3bar"q" - 2bar"p")/(3 - 2)

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

= -19hat"i" + 8hat"j" - 21hat"k"

∴ coordinates of R = (- 19, 8, -21).

Hence, the position vector of R is -19hat"i" + 8hat"j" - 21hat"k" and coordinates of R are (-19, 8, -21).

Concept: Section Formula
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