Question

设平面向量a=(cosx,sinx),b=(cosx+2根号3,sinx),c=(sina,cosa),x∈R

若x∈(0,派/2),证明a和b不可能平行

Answer 1

a=(cosx,sinx), b=(cosx+2√3,sinx), c=(sina,cosa)
let direction of x be i
direction of y be j
direction of x be k

a = (cosx) i + (sinx) j
b = (cosx+2√3) i + ( sinx) j
axb
= {(cosx) i + (sinx)j } x {(cosx+2√3) i + ( sinx) j }
= (cosx. sinx) k - sinx(cosx+2√3)k
= -2√3 k ≠ 0
axb ≠ 0
=> a和b不可能平行

Answer 2

a=(cosx,sinx), b=(cosx+2√3,sinx), c=(sina,cosa)
let direction of x be i
direction of y be j
direction of x be k

a = (cosx) i + (sinx) j
b = (cosx+2√3) i + ( sinx) j
axb
= {(cosx) i + (sinx)j } x {(cosx+2√3) i + ( sinx) j }
= (cosx. sinx) k - sinx(cosx+2√3)k
= -2√3 k ≠ 0
axb ≠ 0
=> a和b不可能平行