15,答案是对的
(1)点积a.b=|a||b|cosθ=√2×1×cos(45°)=√2×1×√2/2=1
|a+b|²=(a+b).(a+b)=a.a+2a.b+b.b=|a|²+2a.b+|b|²=2+2+1=5
|a+b|=√5
(2) (a-b).b=cos90°=0 a.b=b.b=|b|²=1 cosθ=a.b/(|a||b|)=1/√2=√2/2 θ=45°
16.(1)AB=(-3,-4) AC=(c-3,-4) AB.AC=(-3)(c-3)+(-4)(-4)=-3c+25=0 c=25/3
(2)AB=(-3,-4) AC=(c-3,-4)=(2,-4) |AB|=5 |AC|=2√5 AB.AC=-6+16=10
cos角A=AB.AC/|AB||AC|=1/√5
sin角A=2/√5