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NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions

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Question : 14 of 20
Marks: +1, -0
Find the coordinates of the points which trisect the line segment joining the points P(4, 2, –6) and Q(10, –16, 6).
Solution:  
Let R and S be two points which trisect the line segment PQ.
Since PR = RS = SQ
∴ Point R divides the join of PQ in the ratio 1 : 2
∴ Coordinates of R are
(1×10+2×41+2,1×(−16)+2×21+2,1×6+2×(−6)1+2)\left( \frac{1\times10+2\times4}{1+2} ,\frac{1\times(-16)+2\times2}{1+2} ,\frac{1\times6+2\times(-6)}{1+2} \right)
= (6 , - 4 , - 2)
Also, point S divides the join of PQ in the ratio 2 : 1
∴ Coordinates of S are
(2×10+1×42+1,2×(−16)+1×22+1,2×6+1×(−6)2+1)\left( \frac{2\times10+1\times4}{2+1} ,\frac{2\times(-16)+1\times2}{2+1} ,\frac{2\times6+1\times(-6)}{2+1} \right)
= (8 , - 10 , 2)
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