1.

Are the points A (3, 6, 9), B (10, 20, 30) C (25, -41, 5). The vertices of a right angled triangle.

Answer»

By distance formula, 

AB2  = (10 – 3)2  + (20 – 6)2  + (30 – 9)2 

= 49 + 196 + 441 = 686 

BC2  = (25 -10)2  + (- 41 – 20)2  + (5 – 30)2 

= 225 + 3721 + 625 = 4571 

CA2  = (3 – 25)2  + (6 + 41)2  + (9 – 5)2 

= 484 + 2209 + 16 = 2709 

We find that AB2  + CA2  ≠ BC2

(∵ 3395 ≠ 4571) 

∴ ABC is not a right angled triangle.



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