Question

Find the area of triangle formed with points A(1,2,3),B(2,3,1),C(3,1,2).

Answer 1

hope this will help you!!!

Answer 2

The area of triangle formed with points A(1,2,3),B(2,3,1),C(3,1,2).≈ 2.6 sq. units

Step-by-step explanation:

- It is given that the vertices of the Triangle ABC are A(1,2,3), B(2,3,1) and C(3,1,2)​

- The Area of the Triangle is given by,

= 1/2 * ║AB→ X AC→║

AB→ = ( 2-1 , 3-2 , 1-3 )  = (1,1,-2)

AC→ = ( 3-1, 1-2 , 2-3 )  = (2,-1,-1)

║AB→ X AC→║ = ║ i→  j→  k→ ║

                            ║1     1    -2 ║

                            ║2    -1    -1 ║

                         =  i→(-1 - 2) - j→(-1+4) + k→(-1-2)

                         = -3i→ -3j→ -3k→

∴AB→ X AC→ = (-3,-3,-3)

- so, the area of the ΔABC = 1/2║(-3,-3,- 3)||         = 1/2 * √ [(-3)²+(-3)²+(-3)²]

          = 1/2 * √27

            = 1/2 * 3√3

               = 0.5 * 3*1.732

                  = 2.598 sq. units

                 =2.6 sq. units