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

Question : 14

Total: 20

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+2×4

1+2

1×(−16)+2×2

1+2

1×6+2×(−6)

1+2

)

= (6 , - 4 , - 2)
Also, point S divides the join of PQ in the ratio 2 : 1
∴ Coordinates of S are

(

2×10+1×4

2+1

2×(−16)+1×2

2+1

2×6+1×(−6)

2+1

)

= (8 , - 10 , 2)

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