819数学晚自习练习答案抢先版

DAABB BBB

AC CD ABD BCD

3 3010\dfrac {\sqrt{30}} {10} 70 4

(1)
∵a⃗=(1,2,−2),b⃗=(4,−2,4)∴a⃗⋅b⃗=(−3,4−6)\because \vec{a}=(1,2,-2),\vec b =(4,-2,4) \\ \therefore \vec a \cdot \vec b=(-3,4-6)
(2)
∵a⃗=(1,2,−2),c⃗=(3,m,n),when a⃗平行c⃗m=6,n=−6\because \vec a=(1,2,-2),\vec c=(3,m,n),when \space \vec a平行\vec c \\ m=6,n=-6
(3)
∵a⃗=(1,2,−2),b⃗=(4,−2,4)∴a⃗⋅b⃗=1×4+2×(−2)+(−2)×4=−8又∵∣a⃗∣=3,∣b⃗∣=6∴cos<a⃗,b⃗>=−49\because \vec a =(1,2,-2),\vec b=(4,-2,4) \\ \therefore \vec a \cdot \vec b =1 \times 4+2 \times (-2)+(-2) \times 4=-8 \\ 又 \because|\vec a|=3, |\vec b|=6 \\ \therefore cos<\vec a,\vec b>=-\dfrac 4 9