Question

find the area of the triangle whose vertices are (1,2,3) , (2,5,-1) ,(-1,1,2)​

Answer 1

https://www.teachoo.com/3456/748/Example-24---Find-area-of-a-triangle-having-A(1--1--1)--as/category/Examples/

Answer 2

Answer:

6.22

Step-by-step explanation:

Calculate vector by initial and terminal points:

AB = {Bx - Ax; By - Ay; Bz - Az} = {2 - 1; 5 - 2; -1 - 3} = {1; 3; -4}

AC = {Cx - Ax; Cy - Ay; Cz - Az} = {-1 - 1; 1 - 2; 2 - 3} = {-2; -1; -1}

A =  1/2 |AB × AC|

Calculate cross product of vectors:

c = AB × AC

AB × AC =

  i j k

ABx ABy ABz

ACx ACy ACz

 =

  i j k

1 3 -4

-2 -1 -1

 = = i (3·(-1) - (-4)·(-1)) - j (1·(-1) - (-4)·(-2)) + k (1·(-1) - 3·(-2)) = i (-3 - 4) - j (-1 - 8) + k (-1 + 6)  

= {-7; 9; 5}

Calculate magnitude of a vector:

|c| = √[cx² + cy² + cz²]

= √[(-7)2 + 92 + 52] = √[49 + 81 + 25] = √155

Calculate triangle area:

A =  1/2(√155  )

≈6.22 approx

Please find solution pic for clarity