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

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Question : 17
Total: 20
If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(–4, 3b, –10) and R(8, 14, 2c), then find the values of a, b, and c.
Solution:  
Here P(2a, 2, 6), Q(–4, 3b, –10) and R(8, 14, 2c) are vertices of triangle PQR.
∴ Coordinates of centroid of ΔPQR are
(
2a−4+8
3
,
2+3b+14
3
,
6−10+2c
3
)

But it is given that coordinates of centroid are (0, 0, 0)
∴
2a+4
3
 = 0 ⇒ 2a + 4 = 0 ⇒ a = - 2
3b+16
3
 = 0 ⇒ 3b + 16 = 0 ⇒ b =
−16
3
2c−4
3
 = 0 ⇒ 2x - 4 = 0 ⇒ c = 2
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