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Area of plane and equation?
Given:
P(1, 0, 1)
Q(-2, 1, 3)
R(4, 2, 5)
Find the area of PQR and the equation of the plane containing P, Q, & R
1 Answer
- EMLv 78 years agoFavorite Answer
To find the area of the triangle, form vectors from one point to the other 2.
PQ = <-2 - 1, 1 - 0, 3 - 1> = <-3, 1, 2>
PR = <4 - 1, 2 - 0, 5 - 1> = <3, 2, 4>
Area = (1/2)||PQ x PR||
Area = (1/2)||<1(4) - 2(2), 2(3) - (-3)(4), (-3)(2) - 1(3)>||
Area = (1/2)||<0, 18, -9>||
Area = (1/2)sqrt[18² + (-9)²]
Area = 9sqrt(5) / 2
Equation of plane containing P, Q, and R:
18y - 9z = D
Substitute any point to find D (using P here).
18(0) - 9(1) = D
D = -9
18y - 9z = -9
2y - z = -1
