1.已知a=(2,1),与a平行且长度为"二根号五"的向量是:()A.(4,2)B.(-4,-2)C.(2,1)或(-2,-1)D.(4,2)或(-4,-2)2.已知a+b=2i-8j,a-b=-8i+16j,i⊥j,│i│=│j│=1,求a*b./)/).o○(-.-)

Question

1.已知a=(2,1),与a平行且长度为"二根号五"的向量是:( )
A.(4,2) B.(-4,-2) C.(2,1)或(-2,-1) D.(4,2)或(-4,-2)
2.已知a+b=2i-8j,a-b=-8i+16j,i⊥j,│i│=│j│=1,求a*b.
/)/) .o ○
(-.-)

Answer 1

1,设所求向量为ka＝(2k,k),k不为0,则|ka|=4k^2+k^2 开方＝|k|*根号5,由题意,|ka|＝二根号五,所以|k|=2,k=2或-2,选D.
2,因为i⊥j,所以i·j=0,│i│=│j│=1,所以i^2=|i|^2=1,j^2=|j|^2=1,由a+b=2i-8j,两边平方,a^2+2ab+b^2=(2i)^2+2*(2i)*(-8j)+(-8j)^2=4*i^2+0+64*j^2=68,由a-b=-8i+16j,两边平方,a^2-2ab+b^2=(-8i)^2+2*(-8i)(16j)+(16j)^2=64i^2+0+256j^2=320,前式减去后式,2ab-(-2ab)=-252,4ab=-252,ab=-63.