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Area of a triangle made by three points in space

ÀÛ¼ºÀÚ Uploader : corona ÀÛ¼ºÀÏ Upload Date: 2019-01-22º¯°æÀÏ Update Date: 2019-01-22Á¶È¸¼ö View : 313

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When the coordinates of the three points P, Q, and R are respectively as follows, the area of ​​the triangle formed by the three points can be calculated.

P(xp, yp, zp), Q(xq, yq, zq), R(xr, yr, zr)

The cross product (or outer product) of the vectors is:
¡æ
PQ = (a, b, c) = (xq-xp, yq-yp, zq-zp)
¡æ
PR = (d, e, f) = (xr-xp, yr-yp, zr-zp)

¡æ  ¡æ     
PQ¡¿PR =

| i j k |
| a b c | = (b*f-c*e)i - (a*f-c*d)j + (a*e-b*d)k
| d e f |

Thus, the area (A) of the triangle PQR is:

A = (1/2)|PQ¡¿PR|
  = (1/2)*((b*f-c*e)^2 + (a*f-c*d)^2 + (a*e-b*d)^2)^(1/2)


¢º Input the coordinates of points P, Q and R




¡á Vector PQ








¡á Vector PR








¡á Area


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