Question

向量a=(sinc,cosc-2sinc) b=(1,2) 求：若向量a//b tanc=?(2)若|a|=|b| 0

Answer 1

1.

向量a=(sinc,cosc-2sinc) b=(1,2)

向量a//b,则向量a,b的对应坐标成比例.

所以sinc/1=( cosc-2sinc)/2,

即cosc-2sinc=2sinc,cosc=4sinc,

∴tanc=1/4.

2.

若|a|=|b|,

则sin²c+(cosc-2sinc)²=1²+2²,

sin²c+ cos²c-4 cosc sinc+4sin²c=5,

1-4 cosc sinc+4sin²c=5,

-4-4 cosc sinc+4sin²c=0,

-4 cosc sinc+4(sin²c-1)=0,

-4 cosc sinc-4 cos²c=0,

-4 cosc(sinc +cosc)=0,

Cosc=0或 sinc +cosc=0,

因为0