已知向量a=(cos(-θ),sin(-θ)),b=(cos(π/2-θ),sin(π/2-θ) (1)求证:a⊥b (2)若存在不等于0的实数k和t,使a+(t^2+3)b,y=ka+tb,满足x⊥y,试求此时(k+t^2)/t的最小值
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![已知向量a=(cos(-θ),sin(-θ)),b=(cos(π/2-θ),sin(π/2-θ) (1)求证:a⊥b (2)若存在不等于0的实数k和t,使a+(t^2+3)b,y=ka+tb,满足x⊥y,试求此时(k+t^2)/t的最小值](/uploads/image/z/3741771-3-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos%28-%CE%B8%29%2Csin%28-%CE%B8%29%29%2Cb%3D%28cos%28%CF%80%2F2-%CE%B8%29%2Csin%28%CF%80%2F2-%CE%B8%29+%281%29%E6%B1%82%E8%AF%81%EF%BC%9Aa%E2%8A%A5b+%282%29%E8%8B%A5%E5%AD%98%E5%9C%A8%E4%B8%8D%E7%AD%89%E4%BA%8E0%E7%9A%84%E5%AE%9E%E6%95%B0k%E5%92%8Ct%2C%E4%BD%BFa%2B%28t%5E2%2B3%29b%2Cy%3Dka%2Btb%2C%E6%BB%A1%E8%B6%B3x%E2%8A%A5y%2C%E8%AF%95%E6%B1%82%E6%AD%A4%E6%97%B6%EF%BC%88k%2Bt%5E2%29%2Ft%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
已知向量a=(cos(-θ),sin(-θ)),b=(cos(π/2-θ),sin(π/2-θ) (1)求证:a⊥b (2)若存在不等于0的实数k和t,使a+(t^2+3)b,y=ka+tb,满足x⊥y,试求此时(k+t^2)/t的最小值
已知向量a=(cos(-θ),sin(-θ)),b=(cos(π/2-θ),sin(π/2-θ) (1)求证:a⊥b (2)若存在不等于0的实数k和t,使a+(t^2+3)b,y=ka+tb,满足x⊥y,试求此时(k+t^2)/t的最小值
已知向量a=(cos(-θ),sin(-θ)),b=(cos(π/2-θ),sin(π/2-θ) (1)求证:a⊥b (2)若存在不等于0的实数k和t,使a+(t^2+3)b,y=ka+tb,满足x⊥y,试求此时(k+t^2)/t的最小值
1.a=(cos(θ),-sin(θ)),b=(sin(θ),cos(θ)),a*b=0,故a⊥b
2.x*y=k*a^2+t*(t^2+3)b^2=k+t*(t^2+3)=0
(k+t^2)/t=-t^2-3+t=-(t-1/2)^2-11/4
因此最大值是-11/4 没有最小值