P(2, -1, 3), Q(8, 5, -6) and R(4, 1, 0) are the vertices of a
triangle. Show that PQ = 3PR.​

Step-by-step explanation:

Draw diagonal AC

The triangle ABC has sides 17 and 25

Say AB is 17, BC is 25

Draw altitude on side BC from A , say h

h = 17 sin B

Area = 25*17 sin B = 408

sin B = 24/25

In ∆ ABC

Cos B = +- 7/25

= 625 + 289 — b^2 / 2*25*17

b^2 = 914 — 14*17 = 676

b = 26

h = 17*24/25 = 408/25 = 16.32

Draw the second diagonal BD

In ∆ BCD, draw altitude from D, say DE =h

BD^2 = h^2 + {(25 + sqrt (289 -h^2) }^2

BD^2 = 16.32^2 + (25 + 4.76)^2

= 885.6576 + 266.3424

BD = √ 1152 = 33.94 m