Answer to Question #140099 in Analytic Geometry for Faizan butt

Question #140099
Find the area of triangle determinied by the point P(-3,1-1) Q(-2,0,5) and R(-4,-1,2).
1
Expert's answer
2020-10-26T19:00:00-0400

Firstly we should find vectors "\\overline{PQ}" and "\\overline{QR}" :

"\\overline{PQ}=(1,-1,6)"

"\\overline{QR}" "=(-2,-1,-3)"

The area of ​​a triangle PQR is half the area of ​​a parallelogram built on vectors "\\overline{PQ}" and "\\overline{QR}". The area of ​​a parallelogram built on vectors "\\overline{PQ}" and "\\overline{QR}" is the modulus of the vector product "\\overline{PQ}" and "\\overline{QR}", and therefore the area of ​​triangle PQR is:

"S_{PQR}=\\frac{1}{2}|\\overline{PQ}\\times\\overline{QR}|"

"\\overline{PQ}\\times\\overline{QR}=" 9*"\\overline{i}" -9*"\\overline{j}" -3*"\\overline{k}"

"S_{PQR}=\\frac{1}{2}\\sqrt{81+81+9}=\\frac{3\\sqrt{19}}{2}"


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