Engineering
Mathematics
Direction Cosines and Direction Ratio
Section Formulae and Centres of a Triangle
Locus of a Point
Question
Find x if ΔABC is right-angled at A where A ≡ (4,2,3), B ≡ (3,1,8), C ≡ (x,−1,2).
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Solution
In the ΔABC
BC2 = AC2 + AB2
(3 – x)2 + 4 + 36 = 1 + 1 + 25 + (4 – x)2 + 9 + 1
9 + 6x + x2 + 40 = 37 + 16 – 8x + x2
2x = –49 + 37 + 16
= –49 + 53
= 4
x = 2
