Answer to Question #253836 in Electricity and Magnetism for Vitalis

Question

Input data: ax=3, ay=5, az=0, bx=0, by=3, bz=2, cx=5, cy=0, cz=2.
Three points are given with their coordinates. Calculate the data below:
a, The distance between points A and B (dAB).
b, The area of triangle ABC (AABC).
c, The orthogonal projection of vector
r AB
to line AC
à ƒ ƒ ¯ € ¨ à ƒ ƒ ¯ € © ABà ƒ ƒ ¯  ž
r .
d, The angle between vectors
r AB
and
r AC
(à ƒ ƒ Ž ±BAC).
e, The unit vectors that are perpendicular to the plane of triangle ABC (
e1 , e 2
).

Answer 1

a. The distance:

$$dAB=\sqrt{(b_x-a_x)^2+(b_y-a_y)^2+(b_z-a_z)^2},\\ dAB=4.12.$$