1.
AB*AC=20
=>|AB||AC|cosA=20,|AB|=5,|AC|=8
=>cosA=1/2
=>A=60
余弦定理cosA=(b^2+c^2-a^2)/2bc
即:1/2=(25+64-a^2)/80
=> a=7
=>|BC|=7
2.
（2a-b)*b=2abcos@-b^2=2*2*5*cos120-25=-35
3.
a*b=abcos@=3*2*cos60=3
(a+b)^2=a^2+b^2+2a*b=9+4+2*3*2*cos60=19
4.
投影=|a|cos@=4*cos45=2*根號(hào)2 (打不出來,抱歉)
5.
|4a-2b|^2=16a^2+4b^2-16a*b*cos@=768
=>|4a-2b|= 16*根號(hào)3