Find the area of the triangle with vertices

Answered question

2022-02-10

Find the area of the triangle with vertices A(0,0,0), B(2,1,1), and C(−1,−1,−1), and find its angle at the vertex A.

Answer & Explanation

Vasquez

Vasquez

Expert2022-03-13Added 669 answers

Given vertices

A(0,0,0),B(2,1,1),C(1,1,1)

Now,

AB=<20,10,10>=<2,1,1>AC=<10,10,10>=<1,1,1>

Next,

AB×AC=|ijk211111|=i(1+1)j(2+1)+k(2+1)AB×AC=0i+jk

The are of triangle is given as Area, A=12|AB×AC|

so, |AB×AC|=02+12+(1)2=2

Thus, A=12|AB×AC|=12×2=12

A=12

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