Question

数学难题已知向量a已知向量a ＝（√3,-1）向量b ＝（1/2,√3/2）1、求证向量a ⊥向量b2、是否存在实数k

Answer 1

1.a点乘b = √3*(1/2) + (-1) * √3/2 = 0

所以,向量a ⊥向量b

2.x = a - 2b = (√3-1,-1-√3)

y=-ka + b = (-√3k+1/2,k +√3/2)

向量x ⊥向量y ,得到 x点乘y = 0

x点乘y = (√3-1)(-√3k+1/2) + (-1-√3)( k +√3/2) = -4k -2=0

k=-1/2