[题目]如果复数z1,z2,z3满足等式 dfrac (({z)_(2)-(z)_(1))}(({z)_(3)-(z)_(1))}=dfrac (({z)_(1)-(z)_(3))}(({z)_(2)-(z)_(3))}-|||-证明 |(z)_(2)-(z)_(1)|=|z3-(z)_(1)|=|(z)_(2)-(z)_(3)|, 并说明这些等式的-|||-几何意义。