If B is the midpoint of AC, then |AB| = |AC|.
|AB| = 3x + 2
|BC| = 5x - 10
Therefore we have the equation:
3x + 2 = 5x - 10 |subtract 2 from both sides
3x = 5x - 12 |subtract 5x from both sides
-2x = -12 |divide both sides by (-2)
x = 6
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We need the cross product of the two vectors.
a x b
=<2,-2,-3> x <3,2,2>
=
i j k
2 -2 -3
3 2 2
=<-4+6, -(4+9), 4+6>
=<2,-13,10>
The second vector is obtained by reversing the direction, namely <-2,13,-10>
Thus the two vectors are <2,-13,10> and <-2,13,-10>.
