Respuesta :
The Area of the triangle with the given position vectors are; 12.59 sq.units
How to find the area of a triangle?
We are given the position vectors;
A = (3i - 2j + 7k)
B = (2i + 4j + k)
C = (5i + 3j - 2k)
Thus;
AB = B - A
AB = (2i + 4j + k) - (3i - 2j + 7k)
AB = -i + 6j - 6k
BC = C - B
BC = (5i + 3j - 2k) - (2i + 4j + k)
BC = 3i - j - k
CA = A - C
CA = (3i - 2j + 7k) - (5i + 3j - 2k)
CA = -2i - 5j + 9k
Length of AB = √[(-1)² + (6)² + (-6)²]
Length of AB = √73 = 8.544
Length of BC = √[(3)² + (-1)² + (-1)²]
Length of BC = √11 = 3.3166
Length of CA = √[(-2)² + (-5)² + (9)²]
Length of BC = √110 = 10.488
Area of a triangle with 3 side lengths is;
Area = √(s(s - a)(s - b)(s - c))
where; s = (a + b + c)/2
Thus;
s = (√73 + √11 + √110)/2
s = 11.174
Area = √(11.174(11.174 - 8.544)(11.174 - 3.3166)(11.174 - 10.488))
Area = 12.59 sq.units
Read more about Area of Triangle at; https://brainly.com/question/23945265
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