Find the area of a triangle ABC with vertices A (-3,8,7), B (7,1,5), C (-5,10,8).

The area of a triangle built on vectors is found by the formula: S = 1/2 * | AB x AC |;

Find vectors:

AB (10; – 7; – 2), AC (-2; 2; 1);

Find the cross product:

AB x AC = | 10 -7 – 2 |

| -2 2 1 |

= {-3; – 6; 6);

Find the module of the vector product:

| AB x AC | = √ ((- 3) ^ 2 + (-6) ^ 2 + 6 ^ 2) = √ (9 + 36 + 36) = √ (81) = 9;

S = 1/2 * 9 = 4.5.