已知向量a|a|=1,|b|=4,且向量a与...

来源：蜘蛛抓取(WebSpider) 时间：2011-08-27 14:51 标签： 已知a的顶点在原点
已知向量|a|=4,向量|b|=3,向量a垂直向量b的夹角为120度,且向量c=向量a+2向量b,向量d=2向量a+k向量b问当k为何值时,（1）向量c垂直向量d （2）向量c//向量d
a²=16 ,b²=9 ,a•b=|a||b|cos120°=-6.（1）向量c⊥向量d时,c•d=0(a+2 b) •(2 a+k b)=2a²+（k+4）a•b+2kb²=0即：32-6（k+4）+18k=0,k=-2/3.(2) 向量c//向量d,则存在唯一实数t,使得c=td.(a+2 b) =t(2 a+k b)∴1=2t,2=tk.所以k=4.
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/etc/nginx/nginx.conf.已知向量a等于(1,1)2a+b=(4,2),则向量a,b的夹角为
2a+b=2(1,1)+b=(2,2)+b=(4,2).b=(4,2)-(2,2)=(4-2,2-2)=(2,0).a.b=(1,1).(2,0)=1*2+1*0=2.|a|=√(1^2+1^2)=√2.|b|=√(2^2+0)=2.设夹角,则cos=a.b/|a|.|b|=2/2√2.=√2/2.a,b的夹角为π/4.
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顺时针数45度，逆时针数315度按大学的习惯是取逆时针的，中学的忘了啊，毕业太久了 = =
b=(4,2)-2a=(4,2)-(2,2)=(2,0)观察法：a与正X轴45度b与正X轴90度=45度。计算法：Cos=a.b/|a||b|=2/V2*2=V2/2, 则=45度。
b=2a+b-2a=(4,2)-2(1,1)=(2,0)cos＜a,b＞=(a·b)/|a|*|b|=(√2)/2所以夹角是45°
∵向量a=（1,1）设b=(x,y)∴2a+b=(2+x，2+y）=（4,2）即2+x=4
2+y=2解得x=2
y=0∴b=(2,0)所以cos〈a,b〉=a•b∕|a||b|=(1*2﹢1*0)∕(√2*2) =√2／2 所以﹤a,b﹥=45°
b=(2a+b)-2a
=(4,2)-2(1,1)
=(4,2)-(2,2)
=(2,0)cos=a•b/(︱a︱*︱b︱)
=(1,1)&#)/[√(1^2+1^2)*√2^2+0^2]
=√2/2所以=45°
解,设b=(x,y)则由a=(1,1),且2a+b=(4,2)得x+1*2=4,y+1*2=2,则,x=2,y=0.b=(2,0)得cos=a*b/(|a|x|b|)=2/(√2 x2)=√2/2得夹角为π/4
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