Question

已知e1,e2是夹角为60度的单位向量,且a=2*e1+e2,b=-3*e1+k*e2.若｜a+b｜=6,则k=?

Answer 1

e1• e2=1*1*cos60°=1/2.

a=2*e1+e2,b=-3*e1+k*e2,

则a+b=-e1+(k+1)e2.

｜a+b｜=6,则(a+b)^2=36,

[-e1+(k+1)e2] ^2=36,

e1²+(k+1)²e2²-2(k+1) e1• e2=36,

1+(k+1)² -(k+1)=36,

所以k²+k-35=0,k=(-1±√141)/2.